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<< PhysicalConstants`
Set Constant Subscript Pattern Replacements ¯ antiLPattern : x_R := −xL ¯ antiRPattern : x_L := −xR Std. MKS Dimensional Conversions
1 Second 2 JKC := Joule Kilogram Meter
Meter NKC := Newton JKC Joule
Second Second AKC := Ampere Kilogram Meter
1 CKC := Coulomb AKC Ampere Second
Coulomb JKC VKC := Volt Joule CKC
Ampere ^2 NKC HKC := Henry Newton Meter AKC2 Std. MKS Constants Defined or Experimentally Measured MKS Constants
MKS`c = SpeedOfLight;
$Context = "MKS`";
α=FineStructureConstant;
μ0 = VacuumPermeability HKC;
ε0 = VacuumPermittivity HKC; ê
Ω0 = FreeSpaceImpedance HKC 2 ;
el = ElectronCharge; kCoul =HCoulombConstant HKC;ê L
kBoltz = BoltzmannConstant; ê
2 mel = ElectronMass HKC CKC2 ;
mp = ProtonMass; I ê ë M 2 ToE.nb
2 h = PlanckConstant HKC CKC2 ;
h — = I; ê ë M 2 π
GN = GravitationalConstant;
H0 = HubbleConstant; Kilo Meter Convert H0, Mega Parsec Second
70.9711 Kilo Meter B F Mega Parsec Second
a0 = BohrRadius;
R∞=RydbergConstant;
xw = WeakMixingRatio;
θw = ArcSin xw 180 π;
αs = StrongCouplingConstant; B F ê GF = FermiConstant; Convert %,1 Giga eVperC2 2
0.0000116639 eVperC22 AGiga2 ë H L E
mw = WeakBosonMass; Convert %, Mega eVperC2
80 424.8 eVperC2 Mega @ D ParticleData "WBoson", 1 , "Mass"
80 403. @8 < D mz = ZBosonMass; Convert %, Mega eVperC2
91 187.3 eVperC2 Mega @ D ParticleData "ZBoson", "Mass"
91 187.6 @ D mμ = MuonMass; Convert %, Mega eVperC2
105.658 eVperC2 Mega @ D ToE.nb 3
ParticleData "Muon", "Mass"
105.658369 @ D TCMBR = CosmicMicrowaveBackgroundRadiationTemperature ;
New Unit Constants
$Context = "New`"; 4 ToE.nb
A More Natural Reference Model Integrating Relativity, Quantum Mechanics, and M Theory
J Gregory Moxness http://www.TheoryOfEverything.org/TOE/JGM [email protected] DateString
Sun 7 Oct 2007 @D Abstract
M Theory holds the promise of resolving the conflict between general relativity and quantum mechanics but lacks experimental connections to predictability in physics. This connection is made by questioning the value of the traditional Planck unit reference point for the scales at which M Theory operates. It also suggests a cosmological model which has acceleration as being fundamental. It provides for an intuitive understanding of the Standard Model and its relationship to particle masses and the structure of the atom. The prediction of particle mass and lifetimes is a good indicator for its validity. PACS numbers: 03.65, 04.20.-q, 11.25.-w, 11.27.+d, 12.10.-g,12.60.-i, 95.30. 95.35.+d, 95.75.Wx, 98.80-k Keywords: M Theory, Quantum Mechanics, Relativity, Cosmology, Standard Model, CKM, Nuclear Physics
Introduction
This paper will present a new "more natural" reference model for integrating General Relativity (GR) and Quantum Mechanics (QM) by contrasting it with the development of a reference model based on the more traditional Planck units. The new unit-of-measure (UoM) is based on the non-linear expansion or acceleration of the universe [1]. It provides a testable framework for particle mass prediction in support of the Standard Model (SM) as well as M Theory (MT). The fact that the universe is found to be accelerating indicates that an exponential model which accommodates this acceleration could be more natural than the traditional linear model. The key to defining this new model relies on deriving "unity" as the center of scales for length (L), time (T), mass (M), and charge (Q) that are exponentially expanding. Grand Unified Theories (GUTs) hold in high regard the Planck scale for its natural proximity to the unification energies. This scale is
set by setting the fundamental parameters of the velocity of light (c), Planck's constant (Ñ), and Newton's Constant (GN ) to unity. Planck units are derived by combining powers of these constants into their dimensions of L, T, M, and Q. In terms of space-time, it
3 seems to identify a possible lower limit to the length scale at one unit Planck length (lP = GN Ñ c ).
Ñ GN lP = ë c c2
Ñ GN c3
Cosmological models logically define an upper limit based on the age and extent of the universe. In addition to an upper and lower limit (e.g. infinity (¶) and zero=1/¶ respectively), an exponential model should identify a center (unity) in order to be well defined. ToE.nb 5
In physics, the upper limit is naturally thought to be indicated by the macro world of GN and GR. The lower limit is the micro world of Ñ and QM. Fortunately, c is at home in both the micro and macro worlds. In the Planck unit model, the expanse between unity and zero is where GR and QM require the"new physics" beyond SM. As a reference model for scaling the universe, it offers no direct prescription for phenomena associated with atomic scales; therefore, using Planck units as a reference frame for the"center" of an exponentially scaling model seems counter-intuitive. A new model is offered that uses this same general approach in defining natural dimensions but with interesting results achieved by associating with it two more fundamental parameters - the macro Hubble (H0) and the micro fine structure (a). This approach does not detract from the significance of the Planck scale and its associated theoretical frameworks; however, it adds a point of view that puts it properly at the micro edge of an accelerating universal expansion.
Defining The New Model
MKS`α−8
1.24359 μ 1017
Except for the Hubble parameter, the fundamental parameters of Ñ, c, GN , and a are typically thought to be constant. A new model based on an accelerating universe is achieved by considering that all of these fundamental parameters vary with time \footnotetext[2]{Measuring synchronous time variation of multiple fundamental constants is problematic due to the principle of -8 17 covariance. Time variation per tUnit is 1 in a =1.24359 μ 10 .}. It is also necessary to redefine the relationships between the measurable aspects or dimensions of our reality.
Relating Length to Time In Planck units, c sets up the relationship between space and time by being driven to an effective dimensionless unity (a.k.a. geometrized units). This is done by setting unit (Planck) time as that taken by a photon to traverse 1 unit lP, such that tP = lP c. In terms of experimental precision, c is a "defined measurement" with no standard error. That is, its value is used to define length and time by counting its particle/wave oscillations or pulses. ê 2 tP = lP c
Ñ GN H ê L c5
2 Ñ 1 mP = c lP
c Ñ
GN
The concept of using c to drive the relationship of space and time is also used in the new model with the difference focusing on the fact that the universe is found to be accelerating. This new model creates a relationship between the fundamental constants which provides an opportunity to normalize them to that universal acceleration. It does this by defining their magnitudes to be varying with time. For consistency, it also modifies the traditional understanding of the relationship between the dimensionality of L and T. The fundamental "constants" are now more properly referred to as fundamental "parameters". For the assumptions in this new model, acceleration becomes a "dimensionless unity" and requires setting L to be equivalent to the square of the time dimension \footnotetext[3]{Procedural note: in terms of the traditional dimensionality of L, T, M, Q, the extra time dimensions found are associated with the complex plane.}: 6 ToE.nb
1 LTC := LengthUnit TimeUnit2
L = T2 (1)
1 LengthUnit TimeUnit == ∂TimeUnit 2 LTC True
−∂TimeUnit TimeUnit
Â
° ° or alternatively T=L 2 and I= -1 = -T .
With c as the indicator for the expansion of space-time through its integral relationship with the impedance of free space (W0) derived from permittivity (e ) and permeability (m ), it is natural to be defined as covariant with an accelerating universe. Since LT -1=T, c 0ê 0 can also be directly associated with the age of the universe instead of Planck's (dimensionless) unity. Of course, since H0 of dimension T-1 is directly related to the age of the universe, it can be incorporated into the new model as well with \footnotetext[4]{This is an explicit acceleration in terms of dimension and does not rely on the modified relationship between L and T.}:
μ0 := 1 c
ε0 :=μ0 í
Ω0 := μ0 ε0
aU = MKS`c 4 π MKS`H0; ê 2 Convert %, Nano Meter Second
8.6648 Meter Nano SecondA 2 ë E
2 aU = c4p H0 = 1 Unit Accleration = 1 Dimensionless Unit = 8.66 nm s (2)
where: ë t c t_ := 1 t 0
c' @ D ‡ 1&
a l_ := l a'
1&@ D ToE.nb 7
1& H a_ := a H a = t @ D 1& @t D
−H' 1
1&- 0& @ D ° ° c n -H0 n 1 Dimensionless Unit (3) H L
H0 is defined using the space metric (a) which is a function of time. It can also be defined as a function redshift factor (z) as a(z). Depending on cosmological model, this can give the age of the universe:
a 0 tU n (4) H0
The normalization is made possible by (2) and this model's definitionHof:L
c:= α−8 LengthUnit TimeUnit
LengthUnit Solve Convert MKS`c, c, α 8 ; ê TimeUnit
1 α . % B B F F@@ DD 137.036 ê ê α=1 137.0359997094;
Meter Convert c, ê Second
2.99792 μ 108 Meter B F Second
LTC H0 := 4 π c
Kilo Meter Convert H0, Mega Parsec Second
71.5812 Kilo Meter B F Mega Parsec Second
a8 H0 n (5) 4 p tunit
LengthUnit 1 1 c LTC ======α−8 TimeUnit 8 α TimeUnit LTC 4 π H0 True ê 8 ToE.nb
l 1 unit -8 c n n n a tunit (6) 8 a tunit 4 p H0
For the purposes of this work, the assumption is that this relationship is correct and that the analysis of experimental evidence for the constraints on multiple time varying fundamental parameters will corroborate this. -8 A less dramatic alternative is also offered by defining L=T and a dimensionless c n 1 4 p H0 tunit n a . There is evidence from the relationships defined below that this is just as reasonable. This alternative has similar dimensionality to that of the traditional Planck UoM, along with its constant fundamental parameters. Unfortunately, it negates several interesting results related to this model's tie to MT. Some of these results can be recovered by instead relating the 11 MT charge dimensionsê to Degrees of Freedom (DoF). It leaves open the interpretation for the value of a.
The Constancy of Constants
An analysis of the possible time dependence of c, GN , the cosmological constant (L), and the "dark energy" density (rL) has determined [2] that if: ° ° ° rL c GN n 2 - (7) rL c GN
then L is constant. The new model has: ° ° ° c GN rL 1 n - n - n (8) c GN rL tU
implying that is not constant. Current experimental evidence for (and constraints on) the magnitude of the time variation in the fundamental parameters is on the order of 1 part in 1014 per year for G (from type Ia supernova data [3] and 1 part in 1016 per year for a (from quasar dust cloud and fl N Oklo reactor data [4]. Of course, these calculations assumed that the other fundamental parameters were constant. This assumption 9 5 could account for the discrepancy in this model's GN and a varying at 1 part in 10 per year, which is too large by a factor of 10 for 7 GN and 10 for a. In the case where these fundamental parameters are considered unity and constant, as in Natural and Planck UoM, their scaling may be accounted for in the scaling of other related parameters, such as in gauge theories and/or Running Coupling Constants (RCC).
Relating Length to Mass
Typically, equating dimensions of L to M in Planck units uses the QM based Compton effect. Setting Planck's constant (h or Ñ= h p ) 2 and c to unity effectively associates a Compton (wave) length to be the inverse of mass or L=M -1. The association of L to M can also be accomplished in GR by associating mass to its gravitational radius. This method establishes L=M at odds with the Compton 2 method. While this GR approach removes the dimensionality of GN , it leaves a dimensionality to Ñ of L , which is used by Veneziano
[5] to link GR to MT by setting Ñ to the square of string length (lP). Another motivation for Planck units is derived from the fact that
it is only at lP that these two methods for relating length to mass converge.
LengthUnit h:= 4 π c MassUnit 2
h — := H L 2 π ToE.nb 9
Convert —, Kilogram Meter2 Second
1.05457 μ 10-34 Kilogram Meter2 A Second ë E
In the new UoM model, as in Planck units, it uses the Compton effect to set Ñ=clunit munit while giving significantly different results due to c being associated with time and not (dimensionless) unity. This begs the question of whether to simply take the Compton effect as nature's indicator of the dimensional relationship between length and mass. Compton relates mass to a 1D wavelength. In 4D GR space-time, the inter-relationship between mass and gravity is spherically symmetric. The ability to link GR and QM in an intuitive way becomes problematic. A more natural alternative to rationalizing this problem is offered. The Compton effect is the indicator of the inter-dependence between a particle's rest mass and the corresponding quantized wavelength and angle of its emissions. It is merely one aspect of how mass relates to length given the wave-particle duality of nature. It is reasonable to understand a particle's rest mass in terms of both a QM-like linear wave from the Compton effect (L=M-1) and a GR-like point particle from a spherically symmetric volume compression (or deceleration) of space for some period of time. That is:
TimeUnit MTC = MassUnit LTC3 LengthUnit3
MassUnit TimeUnit5
MassUnit 1 LengthUnit3 == ∂TimeUnit MTC 6 LTC3
True
L3 M n n T5 (9) T ° or in terms of a volume of space (V) simply M n V 6. This implies that the transformation of GR space-time into a particle's rest mass is a separate transformation from that of QM transformations to the massless photon (g). This idea is the key to particle mass prediction of the new model. ê Since Ñ is a quantized angular momentum (mvr or spin), its particle dimensionality in the new model is:
MassUnit LengthUnit LengthUnit
MTC TimeUnit LTC LTC
TimeUnit8
ML2 T-1 n T8 (10) which indicates a linkage between QM, GR and an 11D MT space-time with 3 real dimensions of space and 8 dimensions associated with time, but allocated to complex imaginary space.
The model identifies a very natural unit length which is precisely related to the inverse of the Rydberg Constant (R¶):
MKS`α MKS`R∞
6.64984 μ 10-10 Meter 10 ToE.nb
MKS`α == 4 π MKS`a0 SetAccuracy MKS LengthUnit ,20 MKS`R∞ True @ @ D D a 2 h 4 p lunit n n n n 4 p a0 (11) R¶ a cme a cme
This is twice the circumference of the Bohr model of the atom (2 p a0). If this lunit is related to spin (Ñ), it is clear that a fermion of
spin ±Ñ/2 would then be precisely the circumference of the Bohr atom. It should be noted that lunit is being defined using the most -12 accurately measured parameters [6], where Ñ and me are calculated using R¶ known to a standard error of 6.6 ppt or 6.6 10 and a at 0.7 ppb or 7.0 10-10. This is accomplished using the definition of a and the electron or elementary charge (e) less accurately known to 85 ppb:
2 2 2 MKS`el MKS`Ω0 MKS`— == CKC2 4 π MKS`α
True
2 e W0 Ñ = (12) 4 p a
So from (11) and (12) with an error twice that of e's giving 170 ppb accuracy to:
2 MKS`el2 MKS`R∞ MKS`Ω0 MKS`mel2 == CKC2 MKS`α3 MKS`c True
2 2 4 p Ñ R¶ e R¶ W0 e R¶ m0 me n n n (13) a2 c a3 c a3
It is also interesting to note that R¶ is theoretically derived by finding the smallest electron radius of a classical (Bohr orbital) model allowed when incorporating the quantum model using the Hiesenberg uncertainty principle. This may support the idea that the
R¶=a/lunit is more deeply connected to the boundary of both classical-relativistic (macro) and quantum (micro) models of the
universe than lP. ToE.nb 11
The New Model and Special Relativity (SR)
It is instructive to visualize the new model using the concepts of SR. Normalizing c to aU allows for an explicit description of the mechanism for changing a particle's velocity (v). It is done by constraining aU in one or more dimensions. The velocity increases orthogonally to the constraint of aU . The explanation for Lorentz length contraction (l'), time dilation (t'), and increase in mass (m') are a natural result of constraining aU . See Fig. 1.
Fig 1 Visualizing the New Model
Defining Mass' Magnitude Completing a minimally constrained definition in Planck units is accomplished by locking in a specific unit of mass by the free selection of the magnitude for GN = 1. For the most part this affords a pleasing result. Unfortunately, it also results in a unit mass that is significantly larger than the particles of the SM. This large unit mass is rationalized with the hope that it will be the harbinger of particles in a GUT. This indeed may be the case and is not precluded in the definition of the new model.
Since the new UoM-based model is already over-constrained, the ad hoc selection of the magnitude of GN is not possible. The new -1 relationships between L, T, and M give GN a dimension of T , and a new relationship with H0 is possible:
GN n 4 p H0 (14) in terms of both magnitude and dimension. Given accurate current measure of Newton's Constant at 14 ppm [7]:
MKS`GN
6.67422 μ 10-11 Meter3 Kilogram Second2
3 -11 m GN n 6.67422ä10 (15) kg s2 the Hubble parameter can be calculated very precisely in terms of velocity per mega parsec (Mpc) as:
Clear α
@ D 12 ToE.nb
LengthUnit3 MTC Solve Convert MKS`GN, 4 π H0, α 1 ; TimeUnit2 MassUnit LTC3 Kilo Meter ConvertB H0 . %B, F F@@ DD Mega Parsec Second
81.3248 Kilo Meter B ê F Mega Parsec Second
81.3248 km H0 n (16) Mpc s
Convert %,1 Second Abs − 1 HubbleConstantError MKS`H0
2.91773 @ ê D B F ì α=1 137.0359997094;
This preliminary value is outside a rather large standard uncertainty of 5% by a factor of 3 [8], but will be elegantly adjusted in a later 2 section. More detailedê significance of an interestingly small particle size munit=296.7397 eV/c \footnotetext[6]{Representing mass 2 as (eV/c ) is less common than simply (eV). Natural UoM facilitates ignoring fundamental parameters set to unity (Ñ, c, GN ) and equates mass, energy, length and time. This paper exposes the risks of this habit based on UoM assumptions, and attempts to clarify
and maintain complete and accurate representations.} and a rather large tunit=0.2758466 s will also be discussed in a later section.
Defining Charge The magnitude and dimensionality for a unit of charge still needs to be defined explicitly. It has implications for Quantum Field Theory (QFT) linking Quantum ElectroDynamics (QED) to Quantum ChromoDynamics (QCD), particle mass prediction, as well as a more general linkage between GR, QM and MT. In Planck units, charge is essentially a dimensionless parameter. It sets e(Q) to the small fraction 4 pa . Since the dimensionality of M has been redefined in terms of L and T, an alternate definition to the dimensionality of Q is offered with possible implications for Higgs mass prediction.
Ω0 1
True
2 Holding Ω0 to dimensionless unity and using the new model's dimensional definition for M sets the magnitude of e Q n 4 pa Ñ and the dimensionality to:
TimeUnit @ D CTC = ChargeUnit MTC MassUnit ChargeUnit
TimeUnit4
ChargeUnit 1 MassUnit 1 1 LengthUnit3 == ∂TimeUnit == ∂TimeUnit ∂TimeUnit CTC 5 MTC 5 6 LTC3
True
Q n ML-1 2 n MT-1 n L2 n T4 (17)
ê ToE.nb 13
Charge can now be visualized as a measure of the quantum change in particle mass per unit time. In terms of an area (A): ° .. Q n M 5 n V 30 n A. In this model, with the possibility for complex space-time, the quantization of charge seems necessary for the mass transformation between the real spatial dimensions of a 3D GR particle-like volume compression and its dual 1D QM linear wave-like Compton effect. That is: M(3D)/M(1D)=Q(2D)=A=±1 \footnotetext[7]{Obviously, in this context, dimension D=Re[L]=T, ê í or equivalently D n L n T2 if M 3 D n T ÿ M T5 .}.
The significance of an intuitive choice for the magnitude of the charge's mass gives a testable prediction for what may be the mass of the Higgs boson (mH ). This canH be Lshown toI haveM new more natural relationships in the definitions of the Fermi Constant (GF), 0 ElectroWeak (EW) mixing angle (qw), the Vacuum Expectation Value (VEV or v, and
3 mH := 2 — LengthUnit MTC LTC ;
2 Convert mH, Giga eVperC2 ë 147.989 eVperC22 Giga B F
2 Ña 8 p Ñ 1 2 mH n 2 a Ñ lunit n n Ñ = n 147.989 GeV c º (18) R¶ a me c cmunit 2 2 GF
and: ë ê el := 4 πα−7 ChargeUnit;
Convert el, Coulomb
1.60218 μ 10-19 Coulomb @ D This leaves the possibility of a new interpretation for the parameter (4 pa) traditionally equated in a Planck unit model to e2 where Ñ=1.
4 pa me c qunit n e n mH n mH 2 p R¶ n mH a n 4 pa Ñ n 2 a h (19) 2 lunit 2 Ñ
ü EW Mixing Angle (qw) The EW ratio (4pa) from (12) is used to define a weak mixing or Weinberg angle of:
3 απ 2
0.225473 ê
θW = ArcSin %
0.494783 B F
θW 180 π
28.3489 ê 14 ToE.nb
-1 qw n Sin xw n 28.3489 ± (20)
where:
xw n ap 2 n 0.225473 (21)
Surprisingly, this value is easily derived from the standard EW model [9] with a bit of algebraic manipulation, where: ê Clear α
2 g:= @ Del xw CTC
e g n J í í N (22) xw
2 gPrime := el 1 − xw CTC
e g£ n J í í N (23) 1 - xw
using a typical EW SM constraint:
— 1 Solve g xw 8 ,xw 2 Ω0 LTC2 MTC
B p 3 F@@ DD 3 xw Ø a 2
: 3 > xw := απ 2
Ñ ê g n xw 8 (24) W0
Of course, this also agrees with EW SM predictions:
α=1 137.0359997094;
2
ê 2 g gPrime 2 2 el CTC g Sin θW == gPrime Cos θW g2 + gPrime2
TrueH ê L H @ DL H @ DL
gg' £ e n n g Sin qw n g Cos qw (25) g2 + g '2
xw Abs − 1 WeakMixingRatioError MKS`xw
3.86334 B F ì ToE.nb 15
3xw Abs − 1 WeakMixingRatioError 0.22215 + MKS`xw + 0.23124 0.20878 B F ì This prescription for the input parameters of the EW model is within the experimental standard error [6] of 3.4 ppk when averaged
with xw[OnShell]=0.22215 and xw MS]=0.23124. Taking the average of the two xw schemes might be linked to RCC.
@ Completing the Model Combining the discussion of magnitude and dimension above into a single equation, gives:
Clear α
LengthUnit 2 LengthUnit 8 GN := α@ gc2D TimeUnit MassUnit
— 1 gc2 LTC3 1 c LTC ======α−8 TimeUnit MassUnit LengthUnit LTC GN MTC 4 π H0
True ê
LengthUnit3 MTC Solve Convert MKS`GN, 4 π H0, α 8 ; TimeUnit2 MassUnit LTC3 1 α . % B B F F@@ DD 134.867 ê ê α=1 137.0359997094;
h T 8 1 1 8 -8 ê n c n n n 134.867 tunit ºa tunit (26) lunit munit GN 4 p H0
The inverse relationships between the fundamentalI M parameters and a more natural connection between gravitational attraction and Hubble expansion may suggest the duality of MT relating the micro and macro worlds defined above. The proximity of the -8 magnitudes to a tunit may extend the model even further. This exponent seems to support the 8D time construct previously noted in the dimensionality of implying that fine structure is a fractional dimension (fractal) of time. ü Linking GN and qw Dn3+1=4 Dn3+8=11 It is possible to adjust the Newtonian or GR value of GN to the MT value of GN using the dimensionless gravitational 2 8 2 coupling factor for open (go) and closed (gc) strings [11] where gc=go and GN n a gc tunit. A value of:
1 − 2 απ 2 2 gc2 := ë 1 − xw gc2 H ê L
1.13612 16 ToE.nb
p 2 1 - 2 a ÿ p 2 2 1 - 2 a ÿ 2 2 (27) gc n n n 1.13612135987 Cos q 3 p w 1 - a ÿ I M 2 I M Clear α
MKS`GN LengthUnit3 MTC Solve@ConvertD , 4 π H0, gc2 . α→FineStructureConstant TimeUnit2 MassUnit LTC3 α 8 ; B B F 1 α . % ê
137.036F@@ DD ê ê Kilo Meter Convert H0 . %%, Mega Parsec Second
71.5811 Kilo Meter B ê F Mega Parsec Second
% Abs − 1 HubbleConstantError Convert MKS`H0, Kilo Meter Mega Parsec Second
0.171902B F ì B F — 1 gc2 LTC3 1 c LTC ======α−8 TimeUnit MassUnit LengthUnit LTC GN MTC 4 π H0
True ê
2 Convert —, Kilogram Meter2 Second Abs − 1 PlanckConstantError MKS`— A ë E B 1 F ì 5.88235 μ 106 8.04123 μ 10-18 - 1 a16
Convert el, Coulomb Abs − 1 ElementaryChargeError MKS`el
3.31955@ μ 10-8 D 1.17647B μ 107 - 1 F ì a7 2
ê ToE.nb 17
3 2 Convert GN, Meter Second Kilogram Abs − 1 GravitationalConstantError MKS`GN
A ë ë E 2 2 B 1.09459 1017 8 1 p a F ì μ a - 2 71 428.6 - 1
3 1 3 p - 2 a
which alters (21) and shifts the values for H0=71.5811688427 km/s/Mpc and a=1/137.0359997094 in precise alignment with the -11 center of all current experimental values [12]! SM can now be directly linked to GR and MT giving GN =6.67422093862 x 10 m3/kg s.}
Model Detail and Predictions
Combining these discussions of dimensions and magnitude of the fundamental parameters results in an ability to associate the results to familiar arguments as well as predict new relationships in physics.
Charge Predictions The complexity of charge in the SM involves RCC, perturbation theory, Axial-Vector (A-V) currents, quark Cabibbo-Kobayashi- Maskawa (CKM) and neutrino Maki-Nakagawa-Sakata (MNS) phased mixing matrices, Noether's theorem linking conservation rules
and CPT symmetry (and its violations), the Unitary Triangle, a dual Standard Model (dSM), and SU(5)ØSU 3 C×SU 2 I× U 1 Y /6 group theory. The new model builds on this by introducing a simplifying "self dual" Standard Model (sdSM) while predicting and retro or post-dicting the parameters in the theories just mentioned. It solves the hierarchy problem and explains fine tuning of the fundamental parameters. H L H L H H LL ü Linking RCC and xW
Clear α
Solve xw 0.23124, α ; 1 α @. %D
127.037@ D ê ê α=1 137.0359997094; 8 < RCC, with its varying of a at different energies or masses, is a method that accommodates experimental results and provides for the
ê Ñ 1 c Ñ idea of "grand unification" at (or near) the Planck mass (mP n n ) scale. If RCC is viewed as an accommodation of the c lP GN
effect that the accelerating universe has on the fundamental parameters, then by (21), xw and qw will vary with different a. Using this
as a guide to understanding the difference between xw(a)[MS] and xw(a)[OnShell], calculating xw(a)[MS] gives consistent results
with a(MZ)=1/127.037.
αs := xw 2 αs
0.112737 ê 18 ToE.nb
αs Abs − 1 StrongCouplingConstantError MKS`αs 4.21696 B F ì
It will be interesting to see whether the strong coupling constant in the modified-minimal-subtraction scheme as(mZ)[MS]=0.1177(13)
might also relate to as(mZ)[MS]=xw/2=0.1127. The modification of RCC using (21) as an indicator to the path to grand unification is an interesting alternative to current thinking. ü Linking CKM and xW
VCKM =
Vud,Vus,Vub , Vcd,Vcs,Vcb , 8 Vtd,Vts,Vtb 8 < 8 < V8ud Vus Vub < V Vtd Vts Vtb A = KMScale 0.85 λ=KMValues 1, 2 0.221 P T VCKM−λAρη := λ2 1 − , λ,Aλ3 ρ− η , 2 : λ2 −λ,1− ,Aλ2 , : 2 H L> A λ3 1 − ρ+ η , −A λ2,1 : > VCKM9 −λAρηH H LL = 0.97558> 0.221 0.00917478 r -Âh -0.221 0.97558 0.0415149 0.00917478 - h - r + 1 -0.0415149 1 H L It is also found that xw may relate to the Cabibbo angle (qc) in the Wolfenstein parameterization of the CKM matrix [13] where l n Vus n Sin qc. MoreH recent dataL suggests that l n xw may not be outside a rather large standard error of >1% for qc [14]. With d n p 3 = 60é, s n 1 n 2 , r n s , and h=1/( 3 s) gives: A 3 2 † † 2 ∗ Cabbibo and Wienberg Angle relationship xw=SinθC=Sin θW ∗ ê λ := xw H∗ a conjecture about the Unitary Triangle ∗ L H L ToE.nb 19 π δ := ∗ Theoretical Std. Model θγ=60°∗ 3 1 σ := A H L 1 1 ρ := A 4 1 3 η := A 4 3 A = ; 2 π θγ = 60 ; 180 π θγ δ == ArcSin A η 60 180 True @ D π θβ = ; 8 180 % N π 22.5 êê θα = π −θβ−θγ 180 % N π 13 p êê 24 97.5 θβ = ArcSin ρ ; 180 % N π @ D 19.4712 êê θα = π − θβ − θγ; 180 % N π 100.529 êê 4 3 π α π Re VCKM−λAρη 1, 3 == Re Axw ρ− η == α 16 4 True A P TE A H LE 20 ToE.nb VCKM−Play := λ2 1 − , λ,Aλ3 σ − θγ , 2 : λ2 −λ,1− , λ2 , : 2 > A λ3 1 −σ θγ , −λ2,1 : > VCKM9 −PlayI M = 0.974581> 0.225473 0.00573133 - 0.00992695  -0.225473 0.974581 0.0508382 0.0114627 - 0.00992695 Â-0.0508382 1 Abs Re % KMValues ; 1 Abs @ 1 −%@ Dê D 1061.37 49.4045 22.332 49.4045B 5386.35F 9.50767 23.7758 9.50767 832.333 2 1 - l l A ‰- qg l3 s Vud Vus Vub 2 l2 VCKM = Vcd Vcs Vcb = 1 2 = -l - 2 l V V V td ts tb A l3 1 -‰Âqg s -l2 1 (28) 0.974581 0.225473 0.00573133 - 0.00992695  -0.225473 0.974581I 0.0508382M 0.0114627 - 0.00992695 Â-0.0508382 1 where it is interesting to note, VCKM 1, 3 =ap 4 and VCKM 3, 1 =ap 2. The error for each value (in 1/parts per unit) gives: 1061.37 49.4045 22.332 » @ D ê 49.4045» 5386.35@ D 9.50767ê (29) 23.7758 9.50767 832.333 A simpler model which gives the same results, but with a large error in |Vtd|=50% is given where With d n p 3 = 60é, s n 1 n 1, r n s , and h= 3 r) gives:gives: A 2 A = 1; ê VCKM−Play 0.974581 0.225473 0.00573133 - 0.00992695  -0.225473 0.974581 0.0508382 0.00573133 - 0.00992695 Â-0.0508382 1 Abs Re % KMValues ; @ @ Dê D ToE.nb 21 1 Abs 1 −% 1061.37 49.4045 22.332 49.4045B 5386.35F 9.50767 2.08781 9.50767 832.333 0.974581 0.225473 0.00573133 - 0.00992695  -0.225473 0.974581 0.0508382 (30) 0.00573133 - 0.00992695 Â-0.0508382 1 The error for each value (in 1/parts per unit) gives: 1061.37 49.4045 22.332 49.4045 5386.35 9.50767 (31) 2.08781 9.50767 832.333 ü Axial Vector Coupling (CA-V ) It has been found that the Axial-Vector relationship can be defined within experimental error as: Convert VectorAxialCouplingConstant MKS`c2, Mega eVperC2 Centi Meter 3 6.19783 μ 10-44 Centi3 eVperC2 Mega Meter3 A ë H L E 3 3 Convert LengthUnit MassUnit TimeUnit H0 , Mega eVperC2 Centi Meter 5.58369 μ 10-44 Centi3 eVperC2 Mega Meter3 A H L H L E % Abs − 1 VectorAxialCouplingConstantError %% 0.990881 B F ì 3 -44 3 2 CA -V = lunit ÿ H0 tunit ÿ munit = 5.58369 μ 10 cm MeV c (32) ü H FermiL Constant (GF) ë To a posteriori obtain the weak boson masses and the charged lepton masses requires the theoretical derivation of GF and 0 −2 GF := 2 mH 2 Convert GF,1 Giga eVperC2 0.0000114151H L eVperC22 AGiga2 ë H L E 2 5 2 MKS`c MuonLife MKS`mμ 4 Convert 1 4 ,1 Giga eVperC2 8 MKS`— 3 4 π 3 0.000011638 B ì ì H L F 4 H L eVperC28 Giga8 22 ToE.nb 100 4 Convert MKS`GF, 1 Giga eVperC2 8 B ì H L Fì 2 2 5 MKS`c MuonLife MuonMass 4 Convert 1 4 ,1 Giga eVperC2 8 − 1 MKS`— 3 4 π 3 0.222131 B ì ì H L F H L 2 2 100 Convert MKS`GF, 1 Giga eVperC2 Convert GF,1 Giga eVperC2 − 1 2.1792 I A ë H L E ë A ë H L E M G' m -2 F H -5 2 -2 GF = = = 1.16638878775 x10 GeV c Ñ c 3 1 +Dr (33) 8 a -2 º K = 1.14151298702O x10-5 GeV cI2 ë M 2 H L 8 munit 2 2 Abs Convert MKS`GF, 1 Giga eVperC2 ConvertI GF,1ë M Giga eVperC2 − 1 FermiConstantError 2533.95A A ë H L E ë A ë H L E E ë Abs 4 Convert MKS`GF, 1 Giga eVperC2 8 B 2 2 5 MKS`c MuonLife MuonMass 4 ConvertB 1 4 ì H L Fì ,1 Giga eVperC2 8 − 1 MKS`— 3 4 π 3 0.00222131 B ì ì H L F F H L Abs 4 8 Convert GF,1 Giga eVperC2 B 2 2 5 MKS`c MuonLife MuonMass 4 ConvertB 1 ì4 H L Fì ,1 Giga eVperC2 8 − 1 MKS`— 3 4 π 3 % B ì ì H L F F ì 8.62251 H L where Dr=2.1791955% due to radiative corrections in the definition of GF \footnotetext[8]{As explained in footnote 3 2 \footnotemark[6] re: Natural UoM, it is less commonly (but more precisely) represented as GF= Ñc mass . This model explicitly 2 3 defines GF in terms of mH only. Depending on usage, the factor of Ñc is only needed for proper conversions.}. As in the calculation of particles' anomalous magnetic moments (e.g. a ), the radiative corrections are precisely calculated by counting self induced e H L ë perturbations as described in Feynman loop diagrams. Unfortunately, this prescription for Dr is significantly outside the very small H L experimental and theoretical standard error of 8.6 ppm by a factor of 2500. When comparing the non-perturbative GF with an error of ToE.nb 23 2.2 ppk, this error factor is reducted to 9. This error is expected to be rationalized by changes in perturbation theory based on the new model. ü 0 The Vacuum Energy (VEV or v, and The EW Fermi model, mH , e and GF gives: 1 v:= 2 GF Convert v, Giga eVperC2 248.887 eVperC2 Giga @ D 1 3 4 2 v = º 2 mH = 248.887 GeV c (34) 2 GF ê 0 ë Symbolize "<φ >0" := v 2 0 Convert Symbolize "<φ >0" , Giga eVperC2 175.99 eVperC2A Giga E í A A E E v 0 1 4 2 The dual SM (dSM) [15] is based on the SU(5)ØSU 3 C×SU 2 I× U 1 Y /6 group theory. It relates the SU 2 I representation of left-right (L,R) isospin (I), the SU 3 C representation of red-green-blue (r,g,b) color (C), and U 1 Y representation of Yukawa hypercharge (Y) in SU(5). This is done using a diagonal transformation matrix T=(r,g,b,L,R): H L H L H H LL H L ∗ Self Dual SymmetryH L SM ∗ H H LL ∗ SU 5 →SU 3 C×SU 2 I×U 1 Y 6 ∗ H L T : 3 1 1 2 00 C = − 3 − 3 3 H H L H L H L H L ê L TC I M -1 -1200 TI := 0001−1 H L 3 3 TY := 2 111 − 2 − 2 H L TY I M 222-3 -3 TC = Diag -1 3, -1 3, 2 3, 0, 0 H L TI = Diag 0, 0, 0, 1, -1 (36) TY = Diag 1, 1, 1, -3 2, -3 2 H ê ê ê L H L H ê ê L 24 ToE.nb TM := TC TI TY M x_,y_,z_ := xyzH , xyzL × TM 1 1 + xyz × TM 1 2 + xyz × TM 1 3 @ D ¯ 1 1 νR := M 0, −1, 1 ∗ νL:= M 0,1,−1 ∗ 8H 2 L HH L 2 LP TP T HH L LP TP T HH L LP TP T< ¯ νR @ DH @ D L 0, - 1 , 1 2 2 1, 1, 1, -2, -1 ¯9 ¯ = νL := 0 νR ∗νR:=M 0,0,0 ∗ 8 < These matrices are then used with the standard SU(3) monopole representation of each particle m(C,I,Y) producing the SU(5) group monopoles M(r,g,b,L,R)H for that particle.@ TheD specificL transformation is M(r,g,b,L,R)=mC·TC+mI·TI+mY ·TY . For example, the left and right handed spin electrons (eL,R transform as follows: ¯ 1 1 eR := M 0, 1, 1 ∗ eL:= M 0,−1,−1 ∗ 2 M 2 ¯ eR @ DH @ D L 0, 1 , 1 2 2 1, 1, 1, -1, -2 ¯9 ¯ = ¯ eL := νR + eR ∗ M 0,0,1 TY −eR ∗ 8 < ¯ eL H @ D L 0, 0, 1 2, 2, 2, -3, -3 8 < eL = m 0, -1 2, -1 Ø M -1, -1, -1, 2, 1 8 < (37) eR = m 0, 0, 2 Ø M -2, -2, -2, 3, 3 ¯ ¯ ¯ ¯ 0, 0, 1 H ê L H L νR + eR == eL +νL == 2, 2, 2, −3,H −3 L H L True 8 < 8 < ¯ 1 1 dL := M −1, 0, 1 ∗ dR:= M 1,0,−1 ∗ 3 3 M 1, 0, −1 + M 0, 0, 1 @ DH @ D L 1, 0, 0 @-1, -1, 2, 0,D 0 @ D 8 < 8 < ToE.nb 25 1 1 M 1, 0, −1 + 2 M 0, 0, 1 + M 1, 0, −1 3 3 M 1, 0, −1 + 2 M 0, 0, 1 M 1,@ 0, 1 D @ D @ D @1, 0, 1 D @ D @1, 1, 4, -3,D -3 81, 0, 1< 81, 1, 4, -3, -3< 81, 0, 1< 81, 1, 4, -3, -3< ¯8 < d 8L < - 1 ,0, 1 3 3 1, 1, 0, -1, -1 9 = ¯ ¯ ¯ u := d − e 8L L L < ¯ uL 1 ,0, 2 - 3 - 3 -1, -1, -2, 2, 2 ¯9 ¯ = d := d +ν 8R L L < ¯ dR 1 , 1 , 1 - 3 2 - 6 0, 0, -1, 1, 0 9 = ¯ 1 ¯ d8R − M 2,< −3, 1 == − dR +νR 6 True @ D H L ¯ ¯ ¯ uR := uL +νR ¯ uR - 1 , - 1 , - 1 3 2 6 0, 0, -1, 0, 1 9 = ¯ 1 ¯ ¯ ¯ u8R − M 2,< 3, 1 == uL −νL == dL − eR 6 True @ D − ¯ ¯ W R := dR − uR − W R 26 ToE.nb 0, 1, 0 0, 0, 0, 1, -1 8 < − ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ W R == M 0, 1, 0 == dR − uR == dR − dL + eR == eR −νR == dR + uL == dL +νL + uL 8 < ¯ ¯ −dL + uL == νL − eL νL + eR == − νR + eL True @ D H L − W L 0, -1, 0 H 0,L 0, 0, -1, 1 8 ¯ < ¯ W− := d − u 8 L L L< − W L 0, 0, 1 2, 2, 2, -3, -3 8 < ¯ ¯ ¯ ¯ ¯ W− == M 0, 0, 1 == d − u == e == e +ν 8 L < L L L R R True @ D − W R 0, 0, -1 H -2,L -2, -2, 3, 3 8 < W+ := W− 8 R L < + W R H L 0, -1, 0 0, 0, 0, -1, 1 8 + < W L 8 < 0, 1, 0 H 0,L 0, 0, 1, -1 8 < W+ := W− 8 L R < + W L H L 0, 0, -1 -2, -2, -2, 3, 3 8 + < W R 8 < 0, 0, 1 H 2,L 2, 2, -3, -3 8 < 8 < ToE.nb 27 ¯ − + ZL := W L + W L ¯ ZL 0, 0, 0 0, 0, 0, 0, 0 ¯8 <¯ ¯ ZL == −νR + eR −νL + eL == −dL + uL −νL + eL 8 < True ¯ ¯ ¯ ZR := νL + eL +νL + eL ∗ −ZL ∗ ¯ − + ZR := W R + W R H L ¯ ZR 0, 0, 0 0, 0, 0, 0, 0 ¯8 <¯ ¯ ZR == −νL + eL −νR + eR == −dR + uR −νR + eR 8 < True ¯ ¯ ¯ ZL :=νR + eR +νR + eR ∗−ZR ∗ ¯ ¯ ¯ ¯ ¯ −eL == − eL +νL == − eL +νR == eR == eR +νL == eR +νR H L True H L H L ¯ ¯ 0, 0, 0 ZL == −ZR == −ZR == ZL == 0, 0, 0, 0, 0 True 8 < 8 < ¯ ¯ ¯ ¯ 0, 0, 1 νL + eL == −eR == − νL + eL == νR + eR == − νR + eR == 2, 2, 2, −3, −3 True 8 < H L H L H L H L 8 < + 2dL + uL + W L == dL + 2 uL ∗ Beta Decay in Neutron→ Proton ∗ True H L H L dL + 2 uL 1, 1 , 1 2 2 0, 0, 3, -1, -2 9 = 8 < 28 ToE.nb 1 2M 2, −3, 1 + M 2, 3, 1 6 M 2, −1, 1 2 H @ D @ DL 1, - 1 , 1 2 2 @0, 0, 3, -2, Dê-1 9 = 1, 1 , 1 - 2 2 8 < 0, 0, 3, -2, -1 9 = 1 8 M 2, −3,< 1 + 2 M 2, 3, 1 6 M 2, 1, 1 2 H @ D @ DL 1, 1 , 1 2 2 @0, 0, 3, -1,Dê-2 9 = 1, 1 , 1 2 2 8 < 0, 0, 3, -1, -2 9 = 2dL + uL 8 < 1, 1 , 1 - 2 2 0, 0, 3, -2, -1 9 = − 2dL + uL == dL + 2 uL + W L ∗ Beta Decay in Neutron→ Proton ∗ 8 < True H L H L − W L == dL − uL True H L ¯ ¯ νR + eR 0, 0, 1 2, 2, 2, -3, -3 8 < uL + dL 8 < 2 ,0, 1 3 3 0, 0, 2, -1, -1 9 =¯ T ∗ := 3 d 8Y L < ∗ TY -1, 0, 1 3, 3, 0, -3, -3 The sdSM model8 is essentially< the same with the addition of a factor of 3 and 2for TC and TY respectively. In order to maintain SU(5) consistency,8 the typical mC< and mY values also change by an inverse factor (respectively). This has the effect of creating all integer matrices for M and T. More importantly, it maintains integer particle representations of m(C,I,Y) by factoring out simple integer fractions of 1/2 and/or 1/3. ToE.nb 29 It should also be noted that mI is a left handed representation with L=-R. In the absence of isospin, the particle will be right handed. It is this rotational (I) symmetry that represents the assymetry of time (T) due to aU Color is slightly complicated with mC having an even distribution of an arbitrarily chosen (negative) color with a 3-fold degenerate distribution of (r,g, or b) added (or subtracted). It is this translational color symmetry, now labeled as (Clr) in order to avoid confusion upon the introduction of Charge parity (C), that represents the assymetry of sPace parity (P) also due to aU . It establishes a complex linkage with the real dimensions of space (x,y,z), as well as the imaginary (x',y',z') dimensions related to the discussion of (1). This has direct implications for GR and the formation of the more significant mass of the 3 flavor generations and nucleons. Both mI and mC sum to zero within their representations. Hypercharge is more complicated with an even distribution of color (r,g,b) and isospin (L,R) components, which sum to zero across (Clr) and (I). Hypercharge can be said to represent the interchange of color and isospin. In this model, eR=-mY and represents an arbitrarily chosen (negative) hypercharge. The down quark represents a 1/3 interchange of ≤ hypercharge and color dR=(mY -mC)/3. Of course, the W represents the interchange of the up and down quarks, but it is interesting to ≤ ≤ note that they also represent the pure couplings WR =±mY and WL =±mI . Looking into composite 3 quark (baryon) particle 0 r g b 0 + representations, it is interesting to note that nR dR, dL, uR n mC, and DR n 3 dR + WR n 3 mC. As in SM, strong Yukawa hypercharge (Y) and Isospin (I, Ix,y,z, I3) is 0 for generation 2 and 3 particles. Weak Yukawa hypercharge (YW ) and isoTopic spin (T, Tx,y,z, T3) is related Ito strong hyperchargeM and Isospin throughH L qc and the CKM matrix. Space parity and angular momentum quantum numbers In standard representations [16], the principle integer quantum number is n=1 for fundamental SM particles and n¥1 for composite particles. This gives a specific orbital (or azimuthal) angular momentum (L=l-1§n-1=0). The orbital magnetic quantum number (m, not to be confused with the monopole matrix representation above) is -l§m§l. It affects the probability distributions, but not the total momentum of the particles. L+1 Space parity transformation (P) has a translational transformation of Px,y,zØ-Px,y,z and a quantum rotational transformation P= -1 (a.k.a. even or odd parity). P=CT violation is shown by a lack of evidence for right handed neutrinos (nR). "Spin" has horizontal and vertical axial components (sy,z) and vector components along the direction of momentum (sx). A HgenericL representation of a spin axis is (sx,y,z=s3). The specific particle angular momentum is (S=±s3). Total angular momentum (J) is |L-S|§ J§ L+S of dimension Ñ. For fundamental SM particles where n=l=1, L=0, J=S=s. Single SM particle fermions (leptons and quarks) are J=1/2, while single gauge (and Higgs) boson (force) particles are J=1. Leptons have only J transformations. The +(-) or up(down) for the axial spins are also labeled as R(L) handed for the chiral polarizations which have spins parallel (anti- parallel) to the direction of momentum (x). These are typically identified through Stern-Gerlach experiments on accelerated particles. For composite particles made up of multiple fundamental fermions, J is half the difference of left and right handed particles or simply J=|ÒL-ÒR|/2 \footnotetext[9]{Alternate representations: orbital designations from traditional representation in atomic physics for l=1 W to 8 are (S,P,D,F,G,H,I,K) respectively. Other notations have n=s, J=m_l, S=ms, sy,z=sx,y, sx=sz=sp, TZ=I .}. Charge conjugation and time reversal 2 2 L+S Total charge in this model is Q=(I+Y)J of dimension qunit n e . Charge conjugation is C n -1 . C=PT violation is the basis for the weak interactions. I+C The multiplicative parity transformation G n -1 applies only to mesons. The completeH chargeL representation for a particle is often shown as IG J PC . As in translational space transformation, time reversalH L is (TØ-T). Anti-particles (x) are T=CP transformations giving the negative of a particle with oppositeA Ehandedness. The known violations of CP transformations were originally found in the short and long lifetimes 0 0 of the neutral kaons (KS , KL) and more recently in BB mesons from the BaBar collaboration. The arrow of time is intuitively related to the second law of thermodynamics (entropy). This model relates this to the acceleration of the universe as well. This is the basis for the new model's ability to predict the parameters of all particles. The new model's sdSM charge configurations are shown in Table I. ∗ Right−handed neutron or minus right−handed WeakPlus boson & Delta −∇− or minus right−handed electron & Delta −∇− ∗ H H L H L L 30 ToE.nb ∗ ¯ ¯ TC 1 == M 1, 0, 0 2 1 TY − TY 2 1 == − 2dL + uL 2 1 − ¯ ¯ ¯ W L − 3 dL 2 1 eL − 3 dL 2 1 True@@ DD @ D@@ DD@@ DD H @@ DDL@@ DD I M@@ DD@@ DD I M@@ DD@@ DD I M@@ DD@@ DD ∗ Minus left−handed WeakPlus boson or left−handed up minus a down or a left−handed neutrino minus an electron ∗ H − ¯ ¯ TI 1 == M 0, 1, 0 2 1 == W R 2 1 == dR − uR 2 1 == ¯ ¯ L eR −νR 2 1 True@@ DD @ D@@ DD@@ DD @@ DD@@ DD I M@@ DD@@ DD H L@@ DD@@ DD ∗ Minus right−handed WeakPlus boson or minus right−handed Electron or right−handed up minus a down H or a left−handed minus neutrino minus an electron ∗ − ¯ TY 1 == M 0, 0, 1 2 1 == W L 2 1 == eL 2 1 ¯ ¯ ¯ ¯ L dL − uL 2 1 eR +νR 2 1 True@@ DD @ D@@ DD@@ DD @@ DD@@ DD @@ DD@@ DD I M@@ DD@@ DD H L@@ DD@@ DD ¯ νL LeptonL := ¯ eL ¯ νR LeptonR := ¯ eR ¯ uL QuarkL := ¯ dL ¯ uR QuarkR := ¯ dR LeptonL SML := QuarkL LeptonR SMR := QuarkR SML −SMR True SMR −SML True ToE.nb 31 SML 0, 1 , - 1 2 2 -1, -1, -1, 2, 1 0, - 1 , - 1 9 2 =2 8-1, -1, -1, 1, 2< 1 , 1 , 1 9 3 2 6 = 80, 0, 1, 0, -1 < 1 , 1 , 1 9 3 - 2 =6 80, 0, 1, -1, 0< 9 = SMR 8 < 0, 0, 0 0, 0, 0, 0, 0 0, 0, -1 8 < -2, -2, -2, 3, 3 8 < 1 ,0, 2 8 3 3 < 81, 1, 2, -2, -2 < 1 ,0,- 1 9 3 =3 8-1, -1, 0, 1, 1< 9 = 8 < 32 ToE.nb ∗ Proton ∗ P1S1_,S2_ := uS1 + uS2 + dS2 H L P1L,R 1, 1 , 1 2 2 0, 0, 3, -1, -2 9 = P1R,L 8 < 1, 0, 1 1, 1, 4, -3, -3 8 < PS1_,S2_ := 2 uS1 + dS2 8 < PL,R 1, 1, 0 -1, -1, 2, 1, -1 8 < 2M 2, 3, 1 + M 2, 0, −2 6 8 < 1, 1, 0 H -1,@-1, 2, 1, D-1 @ DL ê 8 < M 2, 2, 0 2 8 < 1, 1, 0 @-1, -1, 2,Dê 1, -1 8 < PR,L 8 < 1, - 1 , 3 2 2 2, 2, 5, -5, -4 9 = 2M 2, 0, 4 + M 2, −3, 1 6 8 < 1, 1 , 3 - 2 2 H 2, 2,@ 5, -5, -D4 @ DL ê 9 = M 2, −1, 3 2 8 < 1, 1 , 3 - 2 2 @2, 2, 5, -5, Dê-4 9 = P1L,R + PL,R + P1R,L + PR,L SDSMproton8 =< 1 4, 1, 3 2, 2, 14, -8, -10 8 < 8 < ToE.nb 33 ∗ Neutron ∗ N1S1_,S2_ := dS1 + dS2 + uS2 H L N1L,R 1, - 1 , 1 2 2 0, 0, 3, -2, -1 9 = N1R,L 8 < 1, 0, 0 -1, -1, 2, 0, 0 8 < NS1_,S2_ := 2 dS1 + uS2 8 < NL,R 1, -1, 1 1, 1, 4, -4, -2 8 < 2M 2, −3, 1 + M 2, 0, 4 6 8 < 1, -1, 1 H 1, 1,@ 4, -4, -2 D @ DL ê 8 < M 1, −1, 1 8 < 1, -1, 1 @1, 1, 4, -4, D-2 8 < NR,L 8 < 1, 1 , - 1 2 2 -2, -2, 1, 2, 1 9 = 2M 2, 0, −2 + M 2, 3, 1 6 8 < 1, 1 , 1 2 - 2 H -2,@-2, 1, 2, 1 D @ DL ê 9 = M 2, 1, −1 2 8 < 1, 1 , - 1 2 2 @-2, -2, 1, 2,Dê 1 9 = N1L,R + NL,R + N1R,L + NR,L SDSMneutron8 =< 1 4, -1, 1 -2, -2, 10, -4, -2 8 < ∗ Pion0 ∗ 8 < H L 34 ToE.nb ¯ ¯ uS1 + uS2 − dS1 + dS2 Pion0S1_,S2_ := 2 H L I M Pion0L,L 0, 1 , - 1 2 2 - 2,- 2,- 2,2 2, 2 : > Pion0 : L,R > 0, 0, 0 0, 0, 0, 0, 0 8 < Pion0R,L 8 < 0, 0, 0 0, 0, 0, 0, 0 8 < Pion0R,R 8 < 0, - 1 , 1 2 2 2, 2, 2,-2 2,- 2 : > Pion0L,L + Pion0L,R + Pion0R,L + Pion0R,R SDSMpion0: = > 1 0, 0, 0 0, 0, 0, 0, 0 8 < ∗ PionP ∗ 8 < ¯ Pion+ : u d S1 ,S2 = S1 + S2 H _ L_ Pion+ I ML,L 0, 1 , 1 2 2 I M 1, 1, 1, -1, -2 9 = Pion+ 8 L,R < 0, 1, 0 I 0, 0, 0,M 1, -1 8 < Pion+ 8 R,L < 0, 0, 1 I 2, 2, 2,M-3, -3 8 < Pion+ 8 R,R < I M ToE.nb 35 0, 1 , 1 2 2 1, 1, 1, -1, -2 9 = Pion+ Pion+ Pion+ Pion+ L,L + L,R + R,L + R,R SDSMpionP8 = < 1 0, 2, 2 I M I M I M I M 4, 4, 4, -4, -8 8 < ∗ PionM ∗ 8 < − ¯ Pion S1_,S2_ := uS1 + dS2 H L − Pion L,L H L 0, 1 , 1 - 2 - 2 H -1, -1,L -1, 1, 2 9 − = Pion L,R 8 < 0, 0, -1 H -2, -2,L -2, 3, 3 8 − < Pion R,L 8 < 0, -1, 0 H 0, 0, 0,L-1, 1 8 − < Pion R,R 8 < 0, - 1 , - 1 2 2 H -1, -1,L -1, 1, 2 9 = − − − − Pion L,L + Pion L,R + Pion R,L + Pion R,R SDSMpionM8 = < 1 0, -2, -2 H L H L H L H L -4, -4, -4, 4, 8 8 < ∗ Kaon0 ∗ 8 < ¯ Kaon0S1_,S2_ := dS1 + dS2 H L Kaon0L,L 0, - 1 , 1 2 2 1, 1, 1, -2, -1 9 = Kaon0L,R 8 < 0, 0, 0 0, 0, 0, 0, 0 8 < 8 < 36 ToE.nb Kaon0R,L 0, 0, 0 0, 0, 0, 0, 0 8 < Kaon0R,R 8 < 0, 1 , - 1 2 2 -1, -1, -1, 2, 1 9 = ¯ ¯ d + d − d + d 8 < S1 S2 S1 S2 KaonS0S1_,S2_ := 2 I M I M KaonS0L,L 0, 0, 0 0, 0, 0, 0, 0 8 < KaonS0L,R 8 < 0, 0, 0 0, 0, 0, 0, 0 8 < KaonS0R,L 8 < 0, 0, 0 0, 0, 0, 0, 0 8 < KaonS0R,R 8 < 0, 0, 0 0, 0, 0, 0, 0 8 < ¯ ¯ d + d − d + d 8 < S1 S2 S1 S2 KaonL0S1_,S2_ := 2 I M I M KaonL0L,L 0, 0, 0 0, 0, 0, 0, 0 8 < KaonL0L,R 8 < 0, 0, 0 0, 0, 0, 0, 0 8 < KaonL0R,L 8 < 0, 0, 0 0, 0, 0, 0, 0 8 < KaonL0R,R 8 < ToE.nb 37 0, 0, 0 0, 0, 0, 0, 0 8 < ∗ DeltaPP ∗ 8 < DeltaPPL = 3 uL H L 1, 3 , 1 2 2 0, 0, 3, 0, -3 9 = DeltaPPR = 3 uR 8 < 1, 0, 2 3, 3, 6, -6, -6 8 < %+%% 8 < 2, 3 , 5 2 2 3, 3, 9, -6, -9 9 = ∗ DeltaP ∗ 8 < DeltaPL = 2 uL + dL H L 1, 1 , 1 2 2 0, 0, 3, -1, -2 9 = DeltaPR = 2 uR + dR 8 < 1, 0, 1 1, 1, 4, -3, -3 8 < %+%% 8 < 2, 1 , 3 2 2 1, 1, 7, -4, -5 9 = M 1, 0, 1 8 < 1, 0, 1 @1, 1, 4, -3,D -3 8 < ∗ Delta0 ∗ 8 < Delta0L = 2 dL + uL H L 1, 1 , 1 - 2 2 0, 0, 3, -2, -1 9 = Delta0R = 2 dR + uR 8 < 1, 0, 0 -1, -1, 2, 0, 0 8 < 8 < 38 ToE.nb %+%% 2, - 1 , 1 2 2 -1, -1, 5, -2, -1 9 = ∗ DeltaM ∗ 8 < DeltaML = 3 dL H L 1, - 3 , 1 2 2 0, 0, 3, -3, 0 9 = DeltaMR = 3 dR 8 < 1, 0, -1 -3, -3, 0, 3, 3 8 < %+%% 8 < 2, - 3 , - 1 2 2 -3, -3, 3, 0, 3 9 = Table 1. 8 < Fermions, Neutrinos, Twistors, and Particle-Wave Duality The sdSM charge representation reveals a significant pattern related to neutrinos. Specifically, by adding (or subtracting) the left handed neutrino (nL) to e & d, it will change the LØR (or RØL) symmetry of any particle. This is reversed for the u & W particles. This idea is supported by a suggestion that the left-handed spin electron neutrino (nLe) is made up of a spinless compressed volume of space (a.k.a. particle rest mass m0) oscillating in superposition with gL. As in Penrose' twistor theory [17], where points and lines are duals, the particle and wave are duals of each other. The spinless mass energy of the neutrino is of course equal to the g wave energy by the Compton effect. Twistor theory has a "unassigned" spin 0 particle with homogeneity of -2. The new model suggests this is in fact m0 referenced above. Twistor theory has nLe and nRe with homogeneity -1 and -3 respectively (a difference of m0). Just as a particle-antiparticle fermion pair can be created out of the "vacuum" or with sufficiently energetic photons, the neutrino particle-wave pair can be annihilated by being brought into superposition with its anti-neutrino partner. As in a closed string, "like fermions" cannot be in superposition. This is what differentiates the Bose-Einstein statistics for wave-like bosons from the Fermi- Dirac statistics of the fermions. These fermion masses must be separated at least by the distance of the radius of their wavelength. CPT, Neutrinos, and Left Handed Universal Acceleration Studies of CPT invariance suggests a universal preference for nL. In this model, the photons maintain the horizontal {left - right}=sy n ≤1 2 and vertical up - down n sz n ≤1 2 spin orientations, while the neutrino(s) maintain the helical (or chiral) spin orientation along the axis of momentum sx n ≤1 2 \footnotemark[9]. If the anti-symmetric superposition of m0 and left handed photon (g ) symmetric boson wave becomes the model for the observed left handed spin 1/2 fermion, the definition of the right L ê 8 < ê handed photon (gR) must account for the lack of evidence for nRe. Using the SU(5) charge configurations and turning again to ê Penrose' twistor theory, where the homogeneity of gL and gR are 0 and -4 respectively, it is suggested that the combination emergent from the VEV and time symmetric particle interactions has nLe+ nRe=(0,0,0)=gR. The nLe is stable which means the particle-wave duality does not simply separate or randomly decay into its parts. The lack of evidence for nRe also suggests that the source of stability in nLe is obtained by the assignment of universal acceleration to gL in the particle-wave duality of nLe. This stable acceleration may be visualized as the spiral generated from Golden Sections and Fibonacci numbers. The L-R spin exchange may be visualized as the 3D Lorenz Attractor from chaos theory. This model for particle ToE.nb 39 interaction will be shown to support the transformation of space-time required in the much desired explanation for the measured value of "Dark Energy" contained in L. Particle-Wave Duality and Pilot Wave Theory (PWT) This begins to make clear the paradox of the particle-wave duality. It is consistent with the results of Aspect's experiments on Bell's Inequality and the Einstein-Podolsky-Rosen (EPR) paradox, which reveals that the universe is either deterministically non-local or locally probabilistic with action-at-a-distance [18]. Taking the former view as that of the deBroglie-Bohm and Ghirardi-Rimini- Weber (GRW) PWT [19], this model's description of the neutrino identifies universal acceleration and massless photons as "the guiding waves" and m0 with "the guided particles". Both are needed in order to remain stable in an accelerating universe. Continuing the pattern implies that due to a left handed universal acceleration, eL is a stable superposition of gL and m0 that will be shown to be the inverse of the neutrino mass. The neutrino mass is thus shown to be integrally related to the measured deviations in Ñ m the value of the Bohr magneton (m n e ), understood and precisely calculated theoretically as self induced perturbations (using a B 2 base of a/2p), namely the anomalous magnetic moment of the electron (ae=0.115965218598 %). It is suggested that eR is generated by random superpositions with nLe (eLØeR+nLe). Generating eL out of nR requires the subtraction of nLe or the addition of an anti-neutrino (eRØeL-nLe=eL+nRe). Similar to the polarization of photons, this is the source of randomness found in the spin selection of the electron. Mass Predictions The particle mass predictions are all based relationships with a. Approximations based on the Dokshitzer-Gribov-Lipatov-Altarelli- Parisi (DGLAP) quark-gluon momentum splitting structure functions (using a base of 2a) is also noted when appropriate. ü Unit Mass (mUnit) munit can be defined using the Compton effect: Convert MassUnit, eVperC2 296.74 eVperC2 @ D MKS`mel2 MassUnit2 Convert + , eVperC2 2 MKS`mel MKS`mp Cos θW 296.742 eVperC2 B F @ D 1 Abs 1 −% %% 158 649. B F ê 1 % ElectronMassError 37.0778 êH L Ñ Ñ R a m ¶ e 2 munit n n = n 296.74 eV c lunit c a c 4 p 2 (38) me mne º + n 296.742 eV c2ë 2 mp cos qw m The addition of ne is due to the aforementioned connection with a and m . ë 2 e B ü 40 ToE.nb Weak Bosons (mW ±,Z0}) By standard definition of the EW model, the weak boson masses: gw := xw 2 2 gw mw := GF Convert mw, Giga eVperC2 79.3619 eVperC2 Giga @ D gw 2 4 2 (39) mW ≤ = = º xw 2 2 mH = 79.3619 GeV c G GF F mw ë mz := Cos θW Convert mz, Giga eVperC2 90.1766 eVperC2@ D Giga @ D m ≤ 2 W 2 (40) mZ0 = = 90.1766 GeV c Cos qw GF Abs Convert mw, Giga eVperC2 Convert MKS`mw, Giga eVperC2ë − 1 WeakBosonMassError 4.12981@ @ Dê @ D Dê Abs Convert mz, Giga eVperC2 Convert MKS`mz, Giga eVperC2 − 1 ZBosonMassError 3.46372@ @ Dê @ D Dê Driven by the error in Dr in the definition of GF, the error in this prescription of weak boson masses is outside the experimental standard error of 3.4 ppk by a factor of 4. The new definition of e (already related to GF by mH and a non-unity Ñ) has created an opportunity to simplify the EW model. The standard definition above for gw=xw 2 =e and its role in (39) is based on Natural UoM. Using the new UoM from (18), (19), (22), and (24), then: gw = el; gw = el; 2 2 2 3 Ñ gw CTC == el CTC == g xw 2xw MTC LTC2 True H ê L H ê L J N H L 3 gw n e n g xw n 2 xw Ñ (41) and in terms of g: H L ToE.nb 41 2 mw == g 2 TimeUnit MTC True (42) mW ≤ = 2 gtunit 2 2 mz == gPrime TimeUnit MTC xw True 2 (43) mZ0 = g ' tunit xw ü Charged Leptons (me,m,t) Decay modes of the first generation of SM particles have not been observed, they are stable. Stable Electron Mass (me) By definition in this model, from (13), (19), and (38): 2 2 2hUNITS MKS`R∞ Ω0 el UNITS MKS`R∞ LTC mel = == MTC α2 c α3 c CTC 4 π SetAccuracy@ MassUnit,D 10 @ D α True B F 2 4 p Ñ R¶ e R¶ W0 4 p me n n n munit (44) a2 c a3 c a 3 exactly. Notice the connection to the CKM matrix in that me/munit= 2 xw =8|VCKM[3,1]|=8|Vtd|=16|VCKM[1,3]|=16|Vub|. Also of potential interest, it is found to be approximated by a relationship with DGLAP exponents: 2 2 α − 4 3 MassUnit H L 1835.07H MassUnitê L H L ProtonElectronMassRatio MassUnit 1836.15 MassUnit 1 Abs 1 −% %% 1695.76 B F ê 42 ToE.nb 1 % ElectronMassError 3468.86 êH L - 4 3 2 me º 2 a munit (45) Unfortunately, this interesting prescription is significantly outside theH êveryL small experimental standard error of 170 ppb by a factor of 3470. H L Muon Mass (mm) and Lifetime (tm) In SM, mm,t and tm,t are known relative to GF. Using the Weisskopf-Wigner relation for mass energy, the decay width mass (G) is known as well: 2 MKS`GF2 MKS`mμ5 3 4 π 3 5.36446 μ 10-46 Kilogram2 H L 2 MKS`c2 τμ0 = 1 % MKS`— -6 2.1873 μì10 1 Second2 2 Γμ0 = MKS`c % 655.737 Meter2 H L MuonLife 2.19703 μ 10-6 Second ParticleData "Muon", "Lifetime" 2.19704 μ 10-6 @ D %% %%%% 2 − 1 100 0.444755 H ê L 2 5 Ñ GF mm Gm = º (46) 2 3 c tm 3 4 p -8 -8 In this new model, the stable particle lifetimes increase with tU º 4 pa tunit. This indicates it is reasonable to set te=tp=4 pa tunit. A remarkable pattern is developed, such that each generation (n=1,2,3) ofH chargedL leptons (e,m,t) gives: 2 L n_ := TimeUnit MassUnit11−3 n 2 π 20 π 2 2n π− 1+12 n 3− 1−n 4−n 2 α−8 3−n L n H L H LH Lê H L τ n_ := @ D m n 11−3 n H L H ê L @ D @ D @ D ToE.nb 43 11-3 n 11-3 n 20 t n e,m,t m n e,m,t = tunit munit 2 p ÿ p 2 n2 p- 1+12 n 3- 1-n 4-n 2 a-8 3-n @ 2D @ D H L This single equation reduces the input parameters of the SMH byL three,H L HsuchLê that HonlyL a prescription for the mass (or lifetime) of the leptons is needed. The results for this equation usingK O experimental values for either the mass (or the lifetime) of the charged leptons are within experimental bounds. They are similar in nature to the exponent in the theory of RCC (11-2n f /3), where n f is the number ° of fermions. It indicates a link to an 11D MT. The Mass(V)·Lifetime(t) tied to the suggested 3 real dimensions of space (P) and the 8 imaginary dimensions of time (T) make up the charge (C) configurations listed in Table I. Since the L-R charge configuration does not affect the mass of the particles and the generational impact on mass is significant, it is suggested that it is the number (n-1) of additional compressed imaginary time dimensions (multiplied by a factor of three, one for each real dimension: x,y,z) which is affecting the particle's mass. This defines the limit on the number of particle generations, since n=4 would require more than 11D. 2 Another interesting result is that with t[0]=tunit them m[0]=142.58291278 MeV/c , which is on the order of the pion mass. 4 π m n_ := MassUnit ;n== 1 α 3 m@n_D := m n − 1 ê;n== 2 2 α 1 m@n_D := m @n − 1 Dê; n == 3 8 α 3 me @ D @ Dê mm º (48) 2 a Tau Mass and Lifetime (mt, tt) Following the pattern for mm gives a prescription for the mass of the tau: mm mt º (49) 8 a While the non-perturbative mass and lifetime prescriptions for m and t have an error (<2 %) that is significantly outside the experimental standard error, these values are very consistent with measurement after accounting for the radiative corrections introduced in the standard determination of GF. These charged lepton prescription values are listed in Table II. L 1 8 τ 1 UNITS MKS`mel 8 @ D 1. @ D @ D L 2 5 τ 2 UNITS MuonMass 5 0.994127 @ D @ D @ D L 3 τ 3 UNITS ParticleData "TauLepton", "Mass" Mega eVperC2 2 @ D 1.01253 @ D @ @ D D 44 ToE.nb Table m n , τ n , n, 3 1722.05 MassUnit 1.56274 μ 1018 TimeUnit 353 973.@8MassUnit@ D @ D< 8.526218 Table Convert m n , Mega eVperC2 , Convert τ n , Micro Second , n, 3 0.510999 eVperC2 Mega 4.31077 μ 1023 Micro Second 105.038@8 eVperC2 Mega@ @ D 2.35193 Micro SecondD @ @ D D< 8 Table 2. Mass Lifetime 2 23 me = 0.510999441232 MeV c te = 4.31077 μ 10 M 2 mm = 105.03797892 MeV c tm = 2.35193 Micro Se 2 -7 mt = 1799.2480561 MeV cë tt = 2.82858 μ 10 M ë τ n_ := 4 π α−8 TimeUnit ;n== 1 ë τ n_ := UNITS 2.19703 Micro Second ;n== 2 @ D ê τ n_ := UNITS 290 Femto Second ;n== 3 @ D @ Dê Table m n , τ n , n, 3 @ D @ Dê 1722.05 MassUnit 1.56274 μ 1018 TimeUnit 353 973.@8 MassUnit@ D @ D< 7.964688 Table Convert m n , Mega eVperC2 , Convert τ n , Micro Second , n, 3 0.510999 eVperC2 Mega 4.31077 μ 1023 Micro Second 105.038@8 eVperC2 Mega@ @ D 2.19703 Micro SecondD @ @ D D< 8 ü Uncharged Leptons or Neutrinos (mne,m,t ) 2 2 Given current experimental constraints that all values of ne,m,tº0.3 eV/c with their sum <0.7 eV/c [20], it is suggested that: ∗Neutrino Masses ν el,μ,τ ∗ 2 mνel = MassUnit UNITSH MKS`melL ; H L Convert %, eVperC2 0.172318 eVperC2 ë @ D @ D 2 mνμ = mνel + MassUnit UNITS MuonMass ; Convert %, eVperC2 0.173152 eVperC2 ë @ D @ D ToE.nb 45 2 mντ = mνμ + MassUnit UNITS ParticleData "TauLepton", "Mass" Mega eVperC2 ; Convert %, eVperC2 0.173201 eVperC2 ë @ @ D D @ D m2 unit 2 mne = = 0.172318 eV c me m2 unit -4 2 mnm = mne ≤ = mne ≤ 8.33389 x10ë eV c (50) mm m2 unit -5 2 mnt = mnm ≤ = mnm ≤ 4.95526 x10 eVë c mt ü ë Quark Fermions (mu,d, mc,s, mt,b) Given the ratio of masses in (50), it is interesting to note that from (38}) by rough approximation that: 2 2 2 α − 4 3 MassUnit 6 3.36748Hμê10L MassUnit H L MKS`mp 2 UNITS CKC2 HKC 3.16194Bμ 106 MassUnit2 F 1 Abs 1 − % %% 2 B F 16.3831 H ê L 1 % ProtonMassError 359 050. êH L 2 me mp º (51) munit suggesting that the mass of the first generation of "light quarks" (mu,d) is in some way inversely related to the electron neutrino mass. Generalizing this across the three generations of SM, these baryon masses would be inversely related to neutrino masses with munit and the charged lepton masses as conversion factors. For the precisely measured mp (using me and the electron-proton-mass-ratio with standard error of 460 ppb) (51}) is merely a non-perturbative approximation. Stable First Generation Quark (Up/Down) Mass (mu,d) Simply setting the mass of the down quark (d) to: n− 2−n 2 2 2 1 Qd n_ := Qu n 23−2 n 2 4 J H L Ní @ D @ D 46 ToE.nb 2 md = 2 p me = 3.210704 MeV c (52) and the mass of the up quark (u): ë 1−n 2−n 2 2 1 1 Qu n_ := 2 π 22 n−3 3 π 4 πα H L H Lê 2 @ D 2 mu = md 2 = 1.605352 MeV c (53) give values very close to current measurements and creates a simple relationship that supports the sdSM model of charge and mass prescriptions. ê ë L 1 Qu 1 8 τ 1 UNITS ParticleData "UpQuark", "Mass" Mega eVperC2 8 @ D 0.729705@ D @ D @ @ D D L 2 Qu 2 5 τ 2 UNITS ParticleData "CharmQuark", "Mass" Mega eVperC2 5 @ D 1.07044@ D @ D @ @ D D L 3 Qu 3 2 τ 3 UNITS ParticleData "TopQuark", "Mass" Mega eVperC2 2 @ D 0.997756@ D @ D @ @ D D L 1 Qd 1 8 τ 1 UNITS ParticleData "DownQuark", "Mass" Mega eVperC2 8 @ D 0.642141@ D @ D @ @ D D L 2 Qd 2 5 τ 2 UNITS ParticleData "StrangeQuark", "Mass" Mega eVperC2 5 @ D 1.04686@ D @ D @ @ D D L 3 Qd 3 2 τ 3 UNITS ParticleData "BottomQuark", "Mass" Mega eVperC2 2 @ D 0.768954@ D @ D @ @ D D ∗ Vus=d s ∗ H ê L ToE.nb 47 L 1 Qd 1 8 τ 1 8 @ D 10 819.9@ D MassUnit8 @ D L 2 Qd 2 5 τ 2 5 @ D [email protected] MassUnit5 @ D % %% 5 MassUnit5 5.56552ê 8 MassUnit8 1 % 0.179678 ê 5 MassUnit5 8 MassUnit8 Up Quark Flavor (Up-Charm-Top) Mass (mu,c,t) and Lifetime (tu,c,t) Following the pattern established in (42), using the lepton masses as a basis for the quark masses and assuming the quark lifetimes are the same as the lepton's, a simple quark mass and lifetime pattern emerges: 11-3 n 11-3 n t n u,c,t m n u,c,t =tn u,c,t m n u,c,t ÿ 1-n 2-n 2 2 p 8 1 1 (54) @ D @ D @ D @ D 23-2 n 12 p 4 p a H L H Lê 2 Down Quark Flavor (Down-Strange-Bottom) Mass (md,s,b) and Lifetime (td,s,b) Continuing the pattern for the down series of quarks and using the up flavor series as a basis for the down flavor series: Clear α τ 1 @ D 4 p TimeUnit @ Da8 τ 2 7.96468 μ 10-6 TimeUnit @ D τ 3 1.05131 μ 10-12 TimeUnit @ D 48 ToE.nb 11−3 n test n_ := Simplify Qd n ,Qu n Qd n L n m n 11−3 n test 1 @ D B8 @ D @ Dê @ D< @ D ë @ D F 8 TimeUnit p 8 @ D TimeUnit a8 4 9 8 2 2 p 8 , a8 23 4 ê ê :test 2 > 5 5 p3 5 TimeUnit a2 32 23 20 TimeUnit a2 @ D , 27 20 34 5 34 5 p2 5 ê ê test: 3 ê ê ê ê > TimeUnit a6 256 23 4 TimeUnit a6 @ D , 3 2 3 3 p a ê 3 p :ttest n_ê := Qd n ,Qu n > test 1 @ D 8 @ D @ D< 8 TimeUnit p 8 @ D TimeUnit a8 4 9 8 2 2 p 8 , a8 23 4 ê ê test: 2 > 5 5 p3 5 TimeUnit a2 32 23 20 TimeUnit a2 @ D , 27 20 34 5 34 5 p2 5 ê ê test: 3 ê ê ê ê > TimeUnit a6 256 23 4 TimeUnit a6 @ D , 3 2 3 3 p a ê 3 p :α=1 137.0359997094;ê > 3 π xW = ê α ; 2 test n_ := Qd n ,Qu n test 1 @ D 8 @ D @ D< 2 p, p @ D 8 < ToE.nb 49 test 2 p ,4p 223 4@ D test: ê 3 > 1.8175, 97.8129 @ D It is interesting to note the identification of the EW factor 2 as well as the inverse (or dual) relationships between the up and 8 < 0 down series of quarks, as well as between the leptons and the up series. These values were also guided by the assignment of the mass of the top quark, which nicely closes the sdSM mass progression with its link to mH . These equations give the results in Table III. L n 11−3 n test n_ := Convert Qd n 11−3 n , Mega eVperC211−3 n , τ n L n 11@−3D n 11 3 n Convert@ D Qu: n 11−3 n B @ D, Mega eVperC2 − F τ n @ D test 1 @ D B @ D F> @ D 8 8 3.2107 eVperC28 Mega, 1.60535 eVperC28 Mega @ D test 2 : > 5 5 99.4515 eVperC25 Mega, 1338.05 eVperC25 Mega @ D test 3 : > 3229.61 eVperC22 Mega, 173 809. eVperC22 Mega @ D t n m n 11-3 n =tn m n 11-3 n ÿ : d,s,b d,s,b > u,c,t u,c,t n- 2-n 2 2 2 (55) @ D 23-@2 nD @ D @ D 8 I H L Më Table 3. Quark Masses 2 md = 3.21070418039 MeV c mu = 1.6053520902 M 2 ms = 99.4514789205 MeV c mc = 1338.05427385 M 2 mb = 3229.60822804 MeV ëc mt = 173 809.022825 ë ü ë Composite 2 Quark Hadrons (Mesons) For this section, several important meson particle parameter predictions (PPPs) are reviewed. The branching ratios (Gi/G) and resonant cross sections (sR) for the many decay modes of composite particles are determined from the specific masses and lifetimes. The complete meson PPPs will be reviewed in Appendix A. Pion Mass (mπ0,± ) and Lifetime (τπ0,± ) Speculating on the masses of the pions using the mass relationships above and a modified Weinberg relation [21] gives: 50 ToE.nb = UniversalMassDensityPerExpansion ; −8 3 m±Pion :=α MassUnit gc2 m Pion ± ê 468 288. MassUnit í Convert m±Pion, Mega eVperC2 138.96 eVperC2 Mega @ D mPion := m±Pion gc2 mPion 453 584. MassUnit ì Convert mPion, Mega eVperC2 134.596 eVperC2 Mega @ D 2 2 3 — 6 == α−8 3 MassUnit6 c ê True Ñ2 -8 3 2 (56) mp≤ = gc =a munit gc = 138.959 MeV c c ê where: ì ê ë 2 gc tunit = 4 pH0 = munit = 1 Dimensionless Unit (57) 3 GN lunit and: 2 mp0 = mp≤ gc = 134.596 MeV c (58) This intriguing prescription for the mass of the pion is outside the experimental standard error of 5ppm by a factor of 875. í ë Neutral Kaon Mass (m 0 ) and Lifetime (τ 0 ) KS,L KS,L In order to understand the detail relating to the CPT symmetry and their violations (e.g. CP¨T), it is critical to understand the mass 0 ê 0 ê and (more importantly) the lifetime of (KS(ds-ds)/ 2 , KL=(ds+ds)/ 2 ). ü Composite 3 Quark Hadrons (Baryons) The complete baryon PPPs will be reviewed in Appendix A. Stable Proton Mass (mp) and Radius (rp) The quark composition of the proton has the mass of the up quarks precisely equal to the mass of the down quark. It is this equality that provides for the stability of the proton. Equations (45) and (51) give: ToE.nb 51 2 2 2 α − 4 3 MassUnit 6 3.36748Hμê10L MassUnit H L 2 UNITS MKS`mp HKC CKC2 6 2 3.16194Bμ 10I MassUnitê ë M F m 2 2 e 4 p - 4 3 4 mp º = munit º 2 a munit (59) munit a H ê L 1 Abs H L 1 − % %% 2 B F 16.3831 H ê L 1 % ProtonMassError 359 050. êH L 3 gc2 2 ρc := H0 8 π GN c RH := H0 Clear V 4 π 3 VU := RH 3 @ D MH :=ρcVU MH MU := 4 4 π 3 VP := lP 3 2 MU mP 1.13554 μ 1060 H ê L 3 3 3 rp = Convert % VP, Femto Meter 2 4 π 3 3 3 0.843098 Femto BMeter H L F ì It is interesting to note that by extending this relationship to the 3 generations of SM, the mass of the 3rd generation particles (p+, D++) approach that of the mp. This would suggest that the "Cosmic Egg" or "Primordial Atom" responsible for the "Big Bang (BB)" may have been 3rd generation leptons which would immediately disintegrate into the naturally inflationary accelerating universal 52 ToE.nb expansion of protons and electrons that we know today. It can be shown that when forming a black hole from the current estimate for the mass of the universe derived from the matter density (Wm) and the Hubble radius (RH =c/H0), if compressed into Planck volumes 3 -15 (VP=4p lP /3) each of mass mP, it results in a radius precisely 2 times the proton radius (rp=0.8x10 m). The proton radius' link to the Planck and matter densities is the first indicator of the duality that resolves the hierarchy problem related to VEV, Higgs, and matter densities. Cosmological Predictions This new model is able to give reasonable causes for many cosmological unknowns and their experimentally determined values. ü Milne-Dirac, Eddington, and Weinberg Relations All of these notable physicists attempted to reduce the number of fundamental parameters in physics by creating relationships between them. Some were approximations limited by experimental accuracy. To this end, understanding the intentions as they relate to the new more natural model is interesting. From (14), it is easy to associate this new model to the Milne-Dirac Large Number Hypothesis (LNH) and a time varying GN [22]. Eddington attempted to quantify the LNH with the number of baryons in the universe using a and binary numerology. Unfortunately, 256 he used an integer value of 1/a=136 (and subsequently 137) giving NEddington=137x2 . LNH and NEddington were modified by Weinberg resulting in the relation: 2 3 h H0 º cGN mnucleon (60) while: 2 h H0 3 Convert 3 , Mega eVperC23 c GN 3 207.895 BeVperC23 Mega F h2 H 0 2 mnucleon n 3 n 207.9 eV c (61) c GN is referenced as being "on the order of mp ", yet with current measures of H0 givingë ºmp 3/2, it is not even close to being within current experimental standard error. Following Milne-Dirac, Eddington and Weinberg, the new model offers a better approximation of the pion mass(es) to within 0.4 % using the most accurate current value of a and a binary exponent in MT dimensions, it also gives a very precise value for a large number related to time as: -8 17 Ntime n a n 1.24359 x10 (62) and similar in form to (60), the new model has more precisely: 2 2 GN MassUnit LengthUnit Ñ 4 π H0 c TimeUnit == MassUnit gc2 LengthUnit TimeUnit 1. LengthUnit2 MassUnit LengthUnit2 MassUnit n H L TimeUnit2 TimeUnit2 2 GN munit Ñ 4 p H0 n ctunit n UnitEnergy (63) 2 gc tunit Using the new model's definition for m≤ from (56) gives Weinberg's number (now closely associated with VEV) for the number of p H L nucleons (pions) in the observable universe (MU n MH 4), where MH is the mass in the observable volume of the universe 3 (VU n 4 p RH 3) from Hoyle's Steady State (SS) model and the critical mass energy density of the vacuum ê ë ToE.nb 53 2 Kilogram HKC CKC2 Convert ρc, Meter3 MKS`mp 1B F 6.53729 Meter6 3 g2 2 c rc n H0 (64) 8 p GN Specifically: MU NWeinberg = m±Pion 9.97685 μ 1079 M U 3 8 3 -112 3 79 NWeinberg n = c 8 GN H0 gc a munit = gc a p 2 n 9.97684762939μ 10 ≤ (65) mp ê ê ü I ë M ë ê The New Physics of Black Hole Singularities Given the definition of mass (9) and charge (17), it is proposed that the process for increasing the mass density of a volume is limited ° .. to the stopping of universal acceleration and expansion in the space which that volume occupies (Q n M 5 n V 30 = 0). This would require a compressive force. By SR's link between mass and velocity, if a given mass experiences no compressive force (or ° ° change in velocity) relative to free space (c n c ), it is seen as expanding and accelerating with space. There is no change to its space mass ê í mass density and its charge is 0. Therefore, without invoking "time reversal (T)" symmetries, the lower limit of compressibility in terms of a change in mass density ° ° per unit time is cspace - cmass n 0. The given mass experiences no change in mass density. This is of course a particle traveling at the speed of light (which is the rate of universal expansion as defined above). ° If a given mass experiences maximum compressibility relative to free space, the space it occupies has stopped expanding cmass n 0 ° ° and its mass density changes at the same rate as the universe expands rspace n cspace. The upper limit of compressibility in terms of a ° ° ° change in mass density per unit time is cspace - cmass n rspace - 0 n 1. The given mass and charge is seen as a black hole singularity at the limit of GR physics. This eliminates the need for any "new physics" beyond black hole singularities. It also offers more natural explanations relating to Hawking radiation in the evaporation of black holes, entropy and information loss (or not) in black hole physics. ü The Cosmological Constant In terms of billions of light-years (Gly), the Hubble radius is: Convert RH, Giga LightYear 13.66 Giga LightYear @ D c RH n n 13.66 Gly (66) H0 2 -3 While L is properly defined as an energy (or m=E/c ) per volume (a.k.a. density rL n ML ), its representation varies due to a lack 54 ToE.nb -2 -2 -2 2 of understanding on its origin. It is sometimes represented in terms of dimension L (using RH ) or simply as T (using H0 ) , where the value in this new model can be given as: ρΛ :=ΩΛρc GN Λ := 8 π ρΛ gc2 Convert Λ ,1 Second2 1.6144 μ 10-35 WL A ë E Second2 Λ ρΛ ΩΛ == == 2 c 3H0 ρ WL n 1. WL Clear c t c t_ := 1 t @ D 0 1 ΩΛ@0 =D ‡c t t 0 2 ‡ @ D 3 1 H t_ := 4 π c t 4 π Λ=@ 1D t H t @ D 1 ì ‡ 8 p2 t2 @ D 2 Λ==ΩΛ0 3H t True @ D c:= α−8 LengthUnit TimeUnit G N 2 L n 8 p rL n x3H0 (67) ê 2 gc where the factor x is introduced such that rL n xrc. Another, even more common, representation has: L rL WL n n n x 2 (68) 3 H0 rc The Lambda Cold Dark Matter (LCDM) model of a Friedmann-Lematre-Robertson-Walker (FLRW) metric [22] for a flat accelerating universe has density parameters for energy, matter, and curvature (K): W n Wm +WL n 1 ToE.nb 55 rm Wm =WmDark +WmVisible = =W-x n 1 - x rc K = H0 W-1 = 0 The new model suggests a natural dark energy component originating from universal acceleration that fits very nicely with recent cosmological data [23]: H L 1 WL0 = c dt = 2 3 (70) 0 It is suggested that without visible (baryonic) matter, the dark universe has WmDark 0=1-WL 0=1/3. With the addition of baryons, which ê given the structure of the new sdSM are constructed by adding‡ 2 parts to the universal acceleration (dark energy), which is now in the form of dark neutrino-bound gR while subtracting 1 part m0 and 2 parts gL from the dark matter, which are now visible as baryons. Based on an integer approximation for the measured value of the visible mass in the observable universe: ΩmVisible = 1 24; 1 ΩmDark0 = −ΩΛ0 ê 1 3 3 ΩmDark =ΩmDark0 − ΩmVisible 5 24 Ωm =ΩmDark +ΩmVisible 1 4 ΩΛ = ΩΛ0 + 2 ΩmVisible 3 4 Ω Ω +ΩΛ n m W n 1 WmVisible = 1 24 = 4.166 ... % WL =WL0 + 2 WmVisible = 3 4 = 75 % (71) W =W - 3 W = 5 24 = 20.833 ... % mDark mDark0 mVisibleê W =W +W = 1 4 = 25 % m mDark mVisible ê and using an FLRW age factor of: ê ê Clear a 1 1+z −1 2 a z_ @:=D Ωm a +ΩΛa a 0 êH L a 0 N @ D ‡ ê 1.01379 @ Dêê 56 ToE.nb 1 1+z -1 2 a z = Wm a +WL a da 0 ê 2 1 + WL a 0 =H L ‡ lnK ê n 1.01379O ... 3 WL Wm gives a very precise calculation for the currentH ageL of the universe of: a 0 Convert 1 H0, Giga Year 13.8579 Giga Year @ D @ ê D 109 8 ∗ InverseFineStructureConstantError % Giga 77.6044 Year a 0 tU n n 13 857 928 235 78 years (73) H0 Just as M(3D)/M(1D)=Q(2D)=A, there is an equivalenceH L in this model between r ML-3 n T-1 by a GR conversion, and H L L 4 -4 -4 -2 -2 rL M n L n cT by QM conversions. Getting to the L or T requires selective L=M conversions by assuming gravitational radii and Planck units. Comparing the critical mass density to that of the expected Higgs fieldI shows thatM they are related by a factor of: I M Clear α 2 mH v ρH = @ D 8 4 MassUnitH 4L a16 3 Ñ ρΛ = ΩΛ ρc c 9 MassUnit4 a8 512 p3 2 3 3 ρΛ ρH == H0 TimeUnit 2 2 True ê H ê L α=1 137.0359997094; 8 3 4 3 4 a ê H0 tunit 2 n (74) 9 9 8 p since: H ê L m v 2 m2 4 H H 4 -4 4 rH M = n = mH = 4 a munit (75) 8 4 GF H L I M I M ToE.nb 57 Ñ 3 4 -1 -2 -3 8 rL M = rc WL n rL T = 4 p 3 H0 2 = 9 4 p a 8 tunit (76) c It is shown that instead of a paradoxical disparity in their magnitudes, they are in fact precisely dual. I M I M H ê L ê H L I ë Më ü Gravitational Coupling and String Length In natural units, gc and GN have a direct relationship to the string length (lstring) of order lP. This model has an inverse relationship to time on a universal scale: −8 tstring =α TimeUnit; Convert tstring, Giga Year 1.08777 Giga Year A E 2 lstring = tstring LTC; Convert lstring, Giga LightYear 1.08703 Giga LightYear A E -8 9 9 tstring = 1 4 p H0 =a tunit º 10 yr = lstring = RH 4 p º 10 Gly (77) This is consistent with recent findings related to the large-scale structure of the universe. ê H L ê ü Photon to Baryon Ratio A photon to baryon ratio of: −4 γPerBpm = 2 π α 2.21574 μ 109 9 g Bpn n 2.215 μ 10 (78) is within experimental error. This provides for the opportunity to calculate a precise a(z) which includes the radiation component. This is not included here due to the consideration that theë radiation component is already part of W n Wm +WL n 1 defined above. This increases the age calculations for the early universe at high z. ü Cosmic Microwave Background Radiation (CMBR) 2 PolyLog 4, 1 Gamma 4, 1 MKS`kBoltz4 σSB = 3 2 MKS`— 2 π MKS`c @ D @ D Kilogram2 5.56273 μ 10-8 H L Kelvin8 Second6 2 2 3 σSB SetAccuracy StefanConstant HKC CKC ,11 True B J I M N F 58 ToE.nb MKS`kBoltz Convert MKS`TCMBR , Micro eVperC2 MKS`c2 234.847 eVperC2 Micro B F 2 4 σSB MKS`c Giga 8 MKS`TCMBR4 MKS`c 2 2 MKS`c MKS`— 109 1 H L ì 159.904 Giga 8 Second8 MKS`c Giga Milli % 106 1.87483 Meter Milli 1 8 Second Second8 Recent studies of CMBR by the Wilkinson Microwave Anisotropy Probe (WMAP) have precisely determined its temperature to be é 2 2.72528 K [8]. By Boltzmann's constant (kB), CMBR translates to a mass energy value of 234.8469meV/c . This familiar reference to temperature is a conversion from the determination of the Wien point in the measured Maxwell-Boltzmann blackbody spectrum by 4 Li4 1 G 1 kb using Planck radiation law and the Stefan-Boltzmann constant sSB n represented here in terms of polylogarithms or Ñ3 2 pc 2 deJonquiere's function (which are also related to the Bose-Einstein and Fermi-DiracH L H L statistics mentioned previously). The Wien point was found at wavelength 1.874827 mm (or frequency of 159.9040 GHz). H L From WMAP, the CMBR redshift from first light decoupling from the surface of the universe is z=1089(1). The age of the universe at the time of decoupling is then: z = 1089; a z Convert , Kilo Year H0 506.463 Kilo Year@ D B F a z n 506.4625 kYr (79) H0 1 H L −1 2 aPrime z_ := a Ωm a +ΩΛa a 1 1+z RU = Convert RH Re aPrime z , Giga LightYear @ D ‡ êH L ê 46.9463 Giga LightYear @ @ @ DD D RU DA = Convert , Mega LightYear z + 1 43.07 LightYear Mega B F DL = Convert RU z + 1 , Tera LightYear 51.1715 LightYear Tera @ H L D ToE.nb 59 The comoving radius (RU ), angular size (DA), and luminosity distance (DL) of the observable universe are: £ RU n RH a z n 14.3938 Gpc n 46.9463 Gly RU DA n n 43.07 Mly (80) z + 1 H L DL n RU z + 1 n 51.1715 Tly where: 1 H L -1 £ 2 a z = a Wm a +WL a d a (81) 1 1+z ü H L ‡ ê K ê O Black Hole Evaporation and the Casimir Force Confirmation of the assignment of universal acceleration to a "Theory of Everything (ToE)", is found in the identification of the Casimir force (in a blackbody of the Minkowski vacuum) with that of the gravitational acceleration at the surface of black holes with é a thermalized Hawking radiation (TH ). This is accomplished by applying the Fulling-Davies-Unruh (FDU) effect [24] to both theories where: MKS`c 2 a = 2 π MKS`kBoltz Kelvin MKS`— Meter2 2.46609 μ 1020 Second4 a Ñ é é TFDU n TH n (82) 2 p kB c This results in a thermal bath of Rindler particles (e.g. nRe and unstable protons) in accelerated reference frames with acceleration a K é n 2.466085 x1020 m s2 K é. It should be noted that by definition: l 1 2 ê P ë ë aP = 2 tP LTC 6.36295 μ 1059 2 2 mP c TP = UNITS MKS`kBoltz 4.11437 μ 1025 TempUnit2 @ D 2 2 TP MKS`— SetAccuracy LTC ,77 == UNITS LTC2 aP MKS`kBoltz MKS`c 4.1810893μ 10-69 LengthUnit2 TempUnit2 B F n 4.18109B μ 10-69 TempUnit2 F TimeUnit4 é é 2 p TFDU TP Ñ n = (83) a aP kB c where Planck unit temperature and acceleration are: 60 ToE.nb m c2 é P TP n (84) kB lP aP n (85) 2 tP é Since a black hole increases its thermal radiation as it gets smaller, TP can be characterized as the maximal thermal radiation just before being totally evaporated. Using universal scales in the new model: é é é TFDU n TH n TU (86) resulting from the universal mass now linked to Wm with: MU Ωm VU ρc True MU n Wm VU rc (87) which gives a Casimir blackbody acceleration, or equivalently the acceleration on the surface of a black hole of gravitational radius, which is 1/2 the Schwarzschild radius: GN MU RH π SetAccuracy lstring, −24 gc2 c2 8 2 True B F RS GN MU RH p RBH n n n n lstring n 1.70754 Gly (88) 2 2 gc c 8 2 Using (2) gives an acceleration: H L c4 gc2 aU 2cH0 == SetAccuracy UNITS ,4 4 GN MU 2 π True B B F F 4 c aU n 2 cH0 n (89) 4 GN MU 2 p As done for Planck units, restating this result in terms of the new model gives a surprising result: 2 2 TP MKS`— SetAccuracy LTC ,77 == UNITS LTC2 == aP MKS`kBoltz MKS`c 2 aU MKS`— SetAccuracyB UNITS F B ,72 F MKS`kBoltz MKS`c 4.1810893μ 10-69 LengthUnit2 TempUnit2 B B n 4.18109 μ 10F -69 TempUnitF 2 TimeUnit4 é é é 2 p TFDU TP TU Ñ n n = (90) a aP aU kB c This implies that today the ZPF, VEV, and Ñ represent the minimal change in mass density (charge) from universal acceleration, while black holes represent maximal change in mass density (e.g. where mP is within lP) relative to the current rate of acceleration. ToE.nb 61 These implications will be significant in resolving the debate concerning the origin of inertia, Mach's principle, and an ether related to the ZPF and VEV. ü The Observable Universe at tU£1tUnit 60 In terms of the observable universe today, a black hole of mass MU =1.13554 μ 10 mP, if compressed into as many VP, results in -60 rd sphere of radius 2rp=1.6 fm. This suggests that a BB matter-antimatter vacuum fluctuation resulted in º 10 3 generation primordial atoms of mass mP within universal radius 2rp immediately decayed within tunit. Over time tU they inflated to radius RH with acceleration aU leaving radiation (such as CMBR), leptons (n, e) and baryons (p,n of radius rp). In order to understand the universe at tunit, it is a simple matter to set a=1. This has mP n munit at lunit and is the point where Planck units become synonymous with the new units of this model and where grand unification is realized as a natural result! The observable 60 universe (to a hypothetical observer) is lunit. This begs the question; at tU §1tunit and lU §1lunit, where were today's º 10 mP (then 60 º 10 mUnit) which are currently found within RH ? The answer comes from understanding that rc and Wm can be assigned to VEV (and mH ) by (32). They are either to be found within 2rp as the BB model might suggest or present throughout space-time as VEV (a function of time) which the SS model might suggest. -8 Fundamental parameters and objects scale into fractions as Ntime =a § 1. This model predicts the behavior observed in today's particle accelerators as well as the scaled interactions of the sdSM at tunit, and before. If the universe is non-locally deterministic (by GRW) and spin synchronized (by Bell and Aspect), it logically implies that aU and the laws of physics are non-local. This eliminates the constraint that only interactions which are within a common event's light cone can exhibit similar (not necessarily coherent) behavior. With this, it seems that both BB and SS cosmologies could be synonymous! ü Loop Quantum Gravity (LQG) and an Accelerating Universe The accelerating universe provides for the absolute time lacking in GR without significantly altering the basis for GR's success - namely the space-time metric. It also provides the means for QM to be linked to GR through the FDU effect being equated with both Casimir and Hawking radiation. Quantization is naturally provided by atomic scale unit L, T, M, Q dimensions and unit acceleration. The infinite divisibility of space-time in GR is now limited by the background of an acceleration and its finite measure - time (in tunits). Conclusion To summarize, the new dimensionality relations from (1), (9), and (17): L = T2 M = L3 T-1 = T5 (91) Q = ML-1 2 = MT-1 = T4 The dimensional relationships relate CPT and MT by: ê MT 11 D = C 4 D + P 6 D + T 1 D C Ñ T8 + P L3 n T6 + T 1 (92) H ReL P 3 DH +L Im HT 8 DL H L P x, y, z + iÑ x', y', z' , C SU 5 = r, g, b , L, R I M I M To within all most current experimental error: @ H LD @ H LD H8 The new units to MKS conversions in Table IV have been generated from (73). UNIT to MKS UoM Conversion Constants 62 ToE.nb MKS TimeUnit 0.275847 Second @ D MKS LengthUnit 6.64984 μ 10-10 Meter @ D MKS MassUnit 5.28986 μ 10-34 Kilogram @ D MKS ChargeUnit 1.50032 μ 10-27 Coulomb @ D MKS TempUnit 3.44352 μ 106 Kelvin @ D Table 4. tunit 0.275847 Second -10 lunit 6.64984 μ 10 Meter -34 munit 5.28986 μ 10 Kilog -27 eunit 1.50032 μ 10 Coulo ± 6 Tunit 3.44352 μ 10 Kelvin A comprehensive sdSM prescription for fundamental particles summarized in Table V. This model could be described using terms from [5] as a "one (not-so) constant party view". In this model, the fundamental parameters c, Ñ GN , and H0 are derived from a. It restores the idea of an absolute reference frame for time which is embedded in the very core of these fundamental parameters of physics, which helps in understanding "the arrow of time", entropy and cosmic inflation. The micro and macro scales of the universe are limited in magnitude by time in such a way that infinity becomes only a mathematical concept not physically realized as the universe unfolds. The universe itself becomes the clock upon which time can be measured. \begin{table*} \caption{\label{tab:V}Complete sdSM Prescriptions} \begin{ruledtabular} \begin{tabular}{rlcrrrlr} &[ Mass & Generations & (in $m_{units})\ ]$ & \multicolumn{4}{c}{[$\ \ \ \ $Charge (in $q^2_{units})\ \ \ \ \ $Q=(I+Y)J,$\ \ \ \ J=\left|\#_L-\#_R\right|/2\ \ \ $]}\\ Particle & $1(e)$ & $2(\mu)$ & $3(\tau)$ & $ Q $ & $\Leftarrow m(C,I,Y)\ \ \cdot$ & $J\Rightarrow$ & M(r,g,b,L,R)\\ \hline $\tau$(in $t_{units}$) & $4\pia^{-8}$ & $2((4/9)a/2\pi)^2$ & $(2a)^6/3\pi$\\ \hline $\nu_R=\gamma_R+m_0=0$ & & & & & $2(0,\ \ 0,\ \ 0)\ \ \ $ & $0$ & $(0,0,0,0,0)$\\ $\nu_L=\gamma_L+m_0$ & $1/e$ & $1/e\pm 1/\mu$ & $1/\mu\pm 1/\tau$ & $0$ & $(0,\ \ 1,-1)\ \ \ $ & $1/2$ & $(-1,-1,-1,2,1)$\\ $e_R$ & & & & & $-m_Y=2(0,\ \ 0,-1)\ \ \ $ & $1/2$ & $-T_Y=-(2,2,2,-3,-3)$\\ $e_L=e_R-\nu_L$ & $4\pi/a$ & $3e/2a$ & $\mu/8a$ & $-1$ & $(0,-1,-1)\ \ \ $ & $1/2$ & $(-1,-1,-1,1,2)$\\ \hline ToE.nb 63 $d_R$ & & & & & $2(1,\ \ 0,-1)/3$ & $1/2$ & $(-1,-1,0,1,1)$\\ $d_L=d_R-\nu_L$ & $2u_1$ & $u_2/2^{4-1/4}$ & $u_3/2^{6-1/4} $ & $-1/3$ & $(2,-3,\ \ 1)/3$ & $1/2$ & $(0,0,1,-1,0)$\\ $u_R=d_R+W^+_R=d_R-e_R$ & & & & & $2(1,\ \ 0,\ \ 2)/3$ &$1/2$ & $(1,1,2,-2,-2)$\\ $u_L=u_R+\nu_L$ & $\pi e$ & $4\pi\mu$ & $<\phi^0>_0$ & $+2/3$ & $(2,\ \ 3,\ \ 1)/3$ & $1/2$ & $(0,0,1,0,-1)$\\ \hline $\gamma_R=\nu_L+\overline{\nu}_R$ & & & & & $2(0,\ \ 0,\ \ 0)\ \ \ $ & $1$ & $(0,0,0,0,0)$\\ $\gamma_L=a_U$ & 0 & & & $0$ & $(0,\ \ 1,-1)\ \ \ $ & $1$ & $(-1,-1,-1,2,1)$\\ $W^\pm_R=\pm u_R\mp d_R=-e_R$ & & & & & $\pm m_Y=(0,\ \ 0,\ \ 1)\ \ \ $ & $1$ & $\pm T_Y=\pm(2,2,2,-3,-3)$\\ $W^\pm_L=W^\pm_R\pm 2\nu_L$ & & $2x_w<\phi^0>_0$ & & $\pm 1$ & $\pm m_I=(0,\ \ 1,\ \ 0)\ \ \ $ & $1$ & $\pm T_I=\pm(0,0,0,1,-1)$\\ $Z^0=W^\pm+W^\mp$& & $W^\pm/\cos\theta_w$ & & $0$ & $(0,\ \ 0,\ \ 0)\ \ \ $ & $1$ & $(0,0,0,0,0)$\\ \hline $m_H$ & & $\sqrt{2}a^{-4}$\\ $<\phi^0>_0$ & & $\sqrt{\sqrt{2}}m_H$\\ $x_w=\sin^2 \theta_w$\\ $=\sin\theta_c$ & & $\sqrt[3]{a\cdot\pi/2}$\\ $a_s$& & $x_w/2$\\ \end{tabular} \end{ruledtabular} \end{table*} Table 5. 64 ToE.nb Acknowledgements I would like to thank my family for their love and patience and those in academia who might take the time (and unfortunately risk) to simply help in the review of this work. 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Peebles, Principles of Physical Cosmology (Princeton University Press, 1993). [23] M. Tegmark, D. Eisenstein, W. Hu, and R. Kron, Arxiv preprint astro-ph/9805117 (1998). [24] G. Matsas and D. Vanzella, Arxiv preprint gr-qc/0205078 (2002). ToE.nb 65 Appendix A: Complete PPP These tables are a work in progress. They are generated from Particle Data Group (PDG) experimental data [16]. Specifically, the upgraded file (http://pdg.lbl.gov/2006/mcdata/mass$\_$width$\_$2006.csv ) for use in Monte Carlo based lattice QCD calculations. An improved version of this file (http://www.TheoryOfEverything.org/TOE/JGM/ToE.xls ) is available, which has been created based on this model by generating the data (with few exceptions) from the quark configuration, L and S. Eventually, it will contain all mass, decay width predictions, and error factors. An error factor of §1 is within standard experimental error. An error factor of 0 implies it has yet to be predicted. Setup for PPP Tables 66 ToE.nb PPP vals_ := Text Grid Prepend vals, "Symbol", "CParity", "Isospin", "Hypercharge", @ "IsospinProjection",D "GParity",@ "Parity", "Spin", "Charge", "Mass", "Lifetime", "Width" , Frame@ −> All,@ 8 Background −> None, LightBlue, White , 1 −> LightYellow PPP LeptonQuark Symbol CParity Isospin HypercÖ IsospinÖ GParity Parity Spin Charge Mass Lifetime Width @ D harÖ ProjÖ ge ectiÖ on 0 1 00.10-6 ne ~~ ~~~2 μ ~~ n 0 1 00.μ 10-6 e ~~ ~~~2 ~~ n 0 1 00.μ 10-1 m ~~ ~~~2 ~~ n 0 1 00.μ 10-1 m ~~ ~~~2 ~~ 0 1 00.101 nt ~~ ~~~2 μ ~~ n 0 1 00.μ 101 t ~~ ~~~2 ~~ e 0 1 -1 0.51099Ö ¶ 0. ~~ ~~~2 892 e 0 1 1 0.51099Ö ¶ 0 ~~ ~~~2 892 0 1 1 105.658 2.19704 2.99591 m ~~ ~~~2 - Ö 369 μ μ 10-6 10-16 0 1 1 105.658 2.19704 2.99591 m ~~ ~~~2 Ö 369 μ μ 10-6 10-16 t 0 1 -1 1776.99 2.906 μ 2.265 μ ~~ ~~~2 10-13 10-9 t 0 1 1 1776.99 2.906 μ 2.265 μ ~~ ~~~2 10-13 10-9 u 1 1 1 1 1 2 2.2 ~ 2 3 2 ~ 2 3 ~~ u 1 - 1 - 1 1 1 - 2 2.2 ~ 2 3 2 ~ 2 3 ~~ d 1 1 - 1 1 1 - 1 5.0 ~ 2 3 2 ~ 2 3 ~~ d 1 - 1 1 1 1 1 5.0 ~ 2 3 2 ~ 2 3 ~~ s 0 - 2 0 1 1 - 1 95. ~ 3 ~ 2 3 ~~ ê 2 1 1 s 0 0 1 95. ~ 3 ~ 2 3 ~~ c 0 4 0 1 1 2 1250. ~ 3 ~ 2 3 ~~ c 0 4 0 1 1 2 1250. ~ - 3 ~ 2 - 3 ~~ b 0 1 0 1 1 - 1 4200. ~ 3 ~ 2 3 ~~ b 0 - 1 0 1 1 1 4200. ~ 3 ~ 2 3 ~~ t 0 1 0 1 1 2 174 200. ~ 3 ~ 2 3 ~~ ê t 0 - 1 0 1 1 - 2 174 200. ~ 3 ~ 2 3 ~~ Gauge Boson PPP Table 7. 68 ToE.nb PPP GaugeBoson Symbol CParity Isospin HypercÖ IsospinÖ GParity Parity Spin Charge Mass Lifetime Width @ D harÖ ProjÖ ge ectiÖ on g ~~ 0 ~~~10 0. ~~ g-1 Missing 00~ -11 0 0.μ ¶ 0. UnknÖ 10-16 owÖ n, @ 0, 1 W- ~~ 0 ~~~1 -1 80 403. 3.076 μ 2140. -25 8 Meson PPP Table 8. PPP[Meson] Baryon PPP Table 9. PPP[Baryon]